SAT Nonlinear equations in one variable and systems of equations in two variables Practice Question 15 (Hard)

Question bank / Nonlinear equations in one variable and systems of equations in two variables

Math · Advanced MathHard

In the equation $2x^2 + kx + 8 = 0$ , $k$ is a constant. If the equation has no real solutions, which of the following could be the value of $k$ ?

$-10$

$-8$

$7$

$9$

Show answer and explanation

Answer: C

A quadratic has no real solutions when its discriminant is negative: $k^2 - 4(2)(8) < 0$ , so $k^2 < 64$ and $-8 < k < 8$ . Of the choices, only 7 is in this interval.

Choice B makes the discriminant exactly zero, which gives one real solution, not zero.

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