Quadratic Roots Homework - Mr. Nickels



Quadratic Roots Homework

| |Jacob is solving a quadratic equation. He executes a program on his graphing calculator and sees that the roots are |

| |real, rational, and unequal. This information indicates to Jacob that the discriminant is |

| |(1) zero (3) a perfect square |

| |(2) negative (4) not a perfect square |

| |The roots of the equation [pic] are |

| |(1) real, rational, and equal |

| |(2) real, rational, and unequal |

| |(3) real, irrational, and unequal |

| |(4) imaginary |

| |The roots of a quadratic equation are real, rational, and equal when the discriminant is |

| |(1) –2 (3) 0 |

| |(2) 2 (4) 4 |

| |Which equation has imaginary roots? |

| |(1) [pic] (3) [pic] |

| |(2) [pic] (4) [pic] |

| |The roots of the equation [pic] are real, rational, and equal when a has a value of |

| |(1) 1 (3) 3 |

| |(2) 2 (4) 4 |

| |In the equation [pic] imaginary roots will be generated if |

| |(1) –1 < a –1, only |

| |(2) a < 1, only (4) a < –1 |

| |The equation [pic] has imaginary roots when n is equal to |

| |(1) 10 (3) 6 |

| |(2) 8 (4) 4 |

| |The roots of the equation [pic] are |

| |(1) imaginary |

| |(2) real, rational, and equal |

| |(3) real, irrational, and unequal |

| |(4) real, rational, and unequal |

| |The roots of the equation [pic] are |

| |(1) real and irrational (3) real, rational, and unequal |

| |(2) real, rational, and equal (4) imaginary |

| |Find all values of k such that the equation [pic] has imaginary roots. |

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| |If 2 + 3i is one root of a quadratic equation with real coefficients, what is the sum of the roots of the equation? |

| |Which equation has imaginary roots? |

| |(1) x(5 + x) = 8 (3) x(x + 6) = -10 |

| |(2) x(5 - x) = -3 (4) (2x + l)(x - 3) = 7 |

| |For which positive value of m will the equation [pic] have roots that are real, equal, and rational? |

| |(1) 12 (3) 3 |

| |(2) 9 (4) 4 |

| |The roots of the equation [pic] are |

| |(1) imaginary |

| |(2) real, rational, and equal |

| |(3) real, rational, and unequal |

| |(4) real and irrational |

| |Which statement must be true if a parabola represented by the equation [pic] does not intersect the x-axis? |

| |(1) [pic] |

| |(2) [pic] |

| |(3) [pic] and [pic] is a perfect square. |

| |(4) [pic] and [pic] is not a perfect square. |

|16. If the sum of the roots of [pic] is added to the product of its roots, the result is |

|(1) 15 (3) –2 |

|(2) –15 (4) –8 |

|17. Express, in simplest a + bi form, the roots of the equation [pic] |

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|18. Solve for x in simplest a + bi form: [pic] |

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|19. In physics class, Taras discovers that the behavior of electrical power, x, in a particular circuit can be |

|represented by the function [pic] If [pic] solve the equation and express your answer in simplest a + bi form. |

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|20. Barb pulled the plug in her bathtub and it started to drain. The amount of water in the bathtub as it drains is |

|represented by the equation [pic] where L represents the number of liters of water in the bathtub and t represents the |

|amount of time, in minutes, since the plug was pulled. |

|How many liters of water were in the bathtub when Barb pulled the plug? Show your reasoning. |

|Determine, to the nearest tenth of a minute, the amount of time it takes for all the water in the bathtub to drain. |

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Answers: 1) 3 2) 3 3) 3 4) 3 5) 2 6) 4 7) 1 8) 3 9) 1 10) k>1/3

11) 4 12) 3 13) 1 14) 4 15) 2 16) 4 17) -2 + I, -2-I 18) -4+3i, -4-3i

19) -1 + I sqr(6), -1-I sqr(6)

20) when t = 0, there is 120 liters of water. 4.2 seconds for the bathtub to have no water left

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