Modded SAT Question Bank
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Test
Math
Domain
Advanced Math
Skill
Nonlinear equations in one variable and systems of equations in two variables
Difficulty
Hard
ID: 6011a3f8
Modded SAT Question Bank by Abdullah Mallik

64x2+bx+25=0

In the given equation, b is a constant. For which of the following values of b will the equation have more than one real solution?

  1. -91

  2. -80

  3. 5

  4. 40


Tip: Press CTRL/Command to toggle answer
Correct Answer: A
Rationale

Choice A is correct. A quadratic equation of the form ax2+bx+c=0, where a, b, and c are constants, has either no real solutions, exactly one real solution, or exactly two real solutions. That is, for the given equation to have more than one real solution, it must have exactly two real solutions. When the value of the discriminant, or b2-4ac, is greater than 0, the given equation has exactly two real solutions. In the given equation, 64x2+bx+25=0a=64 and c=25. Therefore, the given equation has exactly two real solutions when b2-46425>0, or b2-6,400>0. Adding 6,400 to both sides of this inequality yields b2>6,400. Taking the square root of both sides of b2>6,400 yields two possible inequalities: b<-80 or b>80. Of the choices, only choice A satisfies b<-80 or b>80.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

Question Difficulty: Hard
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