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POLYNOMIALS4 MARKS QUESTIONS1.?Find all the zeros of the polynomial 2x4?– 11x3?– 16x2?+ 55x + 30 if two of its zeros are √5, ?√5.2.?Find all the zeroes of the polynomials 4x4?+ 14x3?– 38x3?– 28x + 60 if two of its zeroes are √2 & √23.?Find all the zeros of the polynomial x4?– 7x3?+ 7x2?+ 35x – 60, if two of its zeros are √5 and ?√5.4.?Find all the zeroes of polynomial x4?– 4x3?– 35x2?+ 12x + 96 if two of its zeroes are √3 and ?√3.5.?If one zero of the polynomial p(x) = 2x2?– 4kx + 6x – 7 is the negative of other find the zeros of x2?– kx – 1.6.?Find all the zeros of the polynomial 2x4?+ 4x3?– 22x2?– 32x + 48 if two of its zeros are 2√2 and ?2√2.7.?Find all the zeroes of the polynomial x4?– 9x3?+ 27x2?– 33x + 14, if two of its zeroes are 3 ± √2.8.?If two zeros of the polynomial 2x4?– 12x3?– 52x2?+ 276x – 70 are 2 ± √3 find the other zeros.9.?Obtain all the zeros of x4?– 8x3?+3 x2?+ 72x-108 is two of its zeros are 2 and 3.10.?Find the zeros of the polynomial x4?– 5x3?– x2?+ 35x – 42 if √7 & ?√7 are the zeros of the polynomial.11.?Show that 3z + 10 is factor of 9z3?–27z2??-100z + 300. Find also the other factors.12.?If?and?are the roots of 2x2?– 4x + 1 = 0, frame the equation whose roots are??13.?Factorise 3x4?– 10x3?+ 5x2?+ 10x – 814.?If the polynomial x4?– 6x3?+ 16x2?– 25x + 10 is divided by another polynomial x2?– 2x + k, the remainder comes out to x – a, find k and a.15.?If the two zeroes of the polynomial x4?– 8x3?+ 20x2?– 20x + 7 are 3 ±√2, find other zeroes.16.?Obtain all the zeroes of 3x4?+ 6x3?– 2x2?– 10x – 5 if two of its ?zeroes are?17.?Find the zeroes of the polynomial f(x) = x3?– 6x2?+ 11x – 6, if it is given that the product of its two zeroes is 6.18.?If the squared difference of the zeroes of the quadratic polynomial f(x) = x2?+ kx + 30 is equal to 169, find the value of k & the zeroes.19.?If 2 and –2 are the zeroes of the polynomial p(x) = x4?– 5x3+ 2x2?+ 20x – 24, find the other two zeroes.20.?Obtain all the zeroes of x3?– 7x + 6 if one of its zero is 2.3 MARK QUESTINS1.?Divide 26x4?– 13x3?– 74x2?– 46x – 24 by 2x2?– 3x – 5 and verify the result by division algorithm.2.?If one of the zeros of the quadratic polynomial (k – 3)x2?+ 12x + 3 is ?3 find k.3.?What must be subtracted from 8x4?+ 14x3?– 2x2?+ 7x – 8 so that the resulting polynomial is exactly divisible by 4x2?+ 3x – 24.?If α and β are the zeros of the polynomials 3y2?– 8 y + 4, find a quadratic polynomial whose roots are ?5.?Find the zeros of 6√3x2?+ x – 4√3 and verify the relation between their zeros and co-efficient of the polynomial.6.?If α and β are the zeros of the polynomial 20p2?– 15p + 3, find a quadratic polynomial whose zeros are?7.?Find the zeroes of polynomial 4√2x2?+ 20x + 8√2 and verify the relation between the zeroes & co-efficient of the polynomial.8.?Find the zeroes of 3√5x2?– 11x + 2√5 and verify the relationship between the zeroes and co-efficients of the polynomial.9.?Find all other zeroes of the polynomial p(x) = 3x3?-36x +48 of one of its zero is ?410.?What must be added to the polynomial p(x) = 6x4?+ 5x3?? 11x2?– 42x + 9 so that the resulting polynomial is divisible by polynomial Q(x) = x2?+ 3x + 2.11.?Find the value of p for which the polynomial p(x) = 3x3?– 8x2?– 4x – p is exactly divisible by g(x) = 3x + 412.?Divide 7 + 18x + x2?– 4x3?by 3 + 3x – 4x2?and verify the division algorithm.13.?Divide 5 + 14x +2 x2?+4x3?by (3 + 2x – 2x2) and verify the division algorithm.14.?What is the remainder when the polynomial x3?– 2x2?+x – 4 is divided by (x – 2)? What number is to be added to the given polynomial so that (x – 2) is a factor of it?15.?Factorize: x3?+ x2?– 10x + 816.?Factorize: x3?– 5x2?– 2x + 2417.?Find the zeroes of the polynomial f(x) = 3u2?+ 6u and verify the relationship between the zeros and its coefficients.18.?If the zeroes of the polynomial f(x) = x3?– 3x2?+ x + 1 are a – b, a, a + b find a and b.19.?Divide the polynomial f(x) = 10x3?– 5x2?+ 6x – 8 by the polynomial g(x) = 2x + 1 find the quotient & remainder.20.?What ?must be subtracted from the polynomial f(x) = x4?+ 3x3?– 9x2?+ 5x – 6 so that the polynomial is exactly divisible by x2?– 3x + 421. Apply division algorithm to find quotient q(x) and remainder r(x) when the polynomial f(x) is divided by the polynomial g(x).f(x) = x3?– 5x2?+ 8x – 10, g(x) = x2?+ x – 122.?Verify the division algorithm forf(x) = 3x3?– 4x2?+ 6x + 9, g(x) = x ?323.?Find the zeroes of the quadratic polynomial 9x2?– 16 and verify the relationship between the zeroes and its co-efficient.24.?From a polynomial with zeroes ??are roots of polynomial p(x) = ax2?+ bx + c25.?If α and β are the zeroes of the? polynomial x2?+ 3x + 2, form a polynomial whose zeroes are?26.?What should be added to the polynomials 3x4?– 4x2?+ 10x – 5 so that it is exactly divisible by x – 227.?Find the zeroes of the polynomial 4p2?– 4p + 1 and verify the relationship between the zeroes and its co-efficients.28.?Check whether the 1st?polynomial is a factors of the second polynomial or not :29.?Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time and the product of its zeroes are 3, ?8, ?12 respectively.30.?If the zeroes of the polynomial x3?– 3x2?+ x + 1 are p – q, p and p + q, find p and q.MARKS QUESTIONS1Find p if x3?– 3x2?+ px – 8 is divisible by x + 2?2.?Write a quadratic polynomial with zeros 5 + √3 & 5 – √3.3.?If α and β are the zeros of quadratic polynomial 2x2?– 4x + b, find b if 2α + 3β = 8.4.?If α and β are the zeros of the quadratic polynomial x2?– 2x +b; find b if 3α + 2β = 20.5.?If??are the zeros of the polynomial 3x2?+ x + 1 (k – 2) find k.6.?If??are the zeroes of the polynomial 8x2?– 4x + 2(k – 4) find k.7.?Find the HCF of 368 and 24 using division algorithm.8.?If α and β are the roots of the quadratic polynomial p(x) = 3x2?+ (k – 2)x + (3k – 2). Find k if α + β = 2αβ.9.?If one of the zeroes of quadratic polynomial (k – 1)x2?+ kx + 1 is ?5 then find k .10.?If α and β are the roots of the quadratic polynomial p(x) = x2?– (k + 3)x + 2(3k – 4) find k if?.11.?Find m & n12.?α, β are the roots of the polynomial p(x) = 3x2?– (k + 5)x + 3(3k – 2). Find k if?.13.?If α & β are the zeroes of the quadratic polynomial p(x) = 3x2?– (k – 2) x + (3k – 5). Find k if α + β = 3αβ14.?If α and β are the zeroes of the polynomial 3x2?– 7x + k such that 2α ? 3β = 3, find k.15.?If α, β and γ are the zeroes of the polynomial 8x3?+ 4x2?– 3x + 2 find α?1?+ β?1?+ γ?1.16.?Find the zeroes of the quadratic polynomial x2?+ 7x + 10 and verify the relationship between the zeroes and its co-efficients.17.?Find a quadratic polynomial, the sum of whose zeros is 11 and their product is 30. Hence find the zeros of the polynomial.18.?If α and β are the zeros of the polynomial 3x2?– 4x + 7 then find the sum of their reciprocals.19.?The quadratic polynomial p(x) with ?27 as product and 3 as one zero then find the quadratic polynomial.20.?Form a quadratic polynomial whose one of zeros is 7 and the product of zeros is given 28.21.?Find the quotient and remainder when x3?+ 2x2?– x – 4 is divided by x + 2.22.?If one of the root of the equation x2?– 3x + q = 0 is twice other, find the value of q.23.?If the sum and product of the roots of the quadratic equation ax2?– 5x + c = 0 are both equal to 10, then find the values of a and c.24.?Find the GCD of the following?? ? ?m2?– 3m – 18, m2?+ 5m + 625.?Find the value of m in order that (x4?– 2x3?+ 3x2?– mx + 5) may be exactly divisible by (x – 3).26.?Multiply 2x2?– x + 1 by x + 1.27.?Find the HCF and LCM of P(x) = x3?– 8 and Q(x) = x2?– 3x + 2.28.?Multiply?29.?If α and β are the zeroes of quadratic polynomial x2?+ 2x – 3, find??30.?If α and β are the zeroes of the polynomial f(x) = x2?– 3x + k such that α–β = 1 find k.1 MARK QUESTIONS1.?Find the nature of the roots of the quadratic equation x2?+ 10x + 64.2.?Find the nature of zeroes of the quadratic polynomial 2x2?+ 198x + 2544.?Find the degree of the polynomial (x – 1)(x2?+ x – x4?+ 2)5.?If one of the zeros of the quadratic polynomial (k + 3) x2?+ kx + 3 is ?2 find k.6.?Find the no. of zeroes of y = f(x)7.?Find the quadratic polynomial whose zeroes are ?2 & 3.8.?Find a quadratic polynomial whose zeroes are 2 + √3 and 2 – √39.?Frame a quadratic polynomial p(x) whose sum of zeroes is ?3 and product of zeroes is ?2/3.10.?Find the no. of zeroes of the polynomial y = f(x)11.?Find the zeroes of the polynomial 3x2?– 4 x – 412.?If ?3 is a zero of the polynomial x2?+ x – (3 + 2k) then find the value of k.13.?Find a quadratic polynomial whose sum of zeros is ?12 and product is 14.14.?The HCF & LCM of two numbers are 8 and 80. If one of the numbers is 16, find the other.15.?If f(x) = x + 1, then 3f(2) – 2f(3) = _______(a)??????? 0 ? ? ? (b)???? 1 ? ? ? ? ?(c)????? 2 ? ? ? ? ? ?(d)???? 316.?If ?f(x) = x3?– 3x2?+ 3x = 1, then f(3/2) = ______.17.?If x = 1 is a zero of the polynomial F(x) = x2?– 5x + k, then the value of k is:(a)??????? 4 ? ? ? ? ? (b)???? ?4 ? ? ? ? ?(c)????? 6 ? ? ? ? ? ? (d)???? ?618.?If (x – 2) is one factor of the polynomials x2?+ ax – 6 and x2?– 9x + b, then a + b is equal to :(a) ? 15 ? ? ? ? ? ? ?(b) ? ?13 ? ? ? ? ? ?(c) ? ?11 ? ? ? ? ? (d) ? 1019.?The roots of the equation ax2?+ bx + c = 0 will be reciprocal of each other if :(a)??????? a = b???????????????????? (b)???? a = bc(c)??????? a = c???????????????????? (d)???? b = c20.?If the sum of the zeroes of the quadratic polynomial f(x) = kx2?– 2x + 3 is 3 find k. ................
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