If there are two unique solutions to the equation x^2 + bx + 9 = 0, wh

Question

If there are two unique solutions to the equation x^2 + bx + 9 = 0, which of the following could not be a value of b?

A. -10
B. -6.5
C. -6
D. 6.5
E. 10

houston1980 · Answer

Quadratic equation have a single solution when b^2 - 4ac = 0 OR when b^2 = 4ac

In the above equation 4ac = 4*1*9 = 36

Only option C is b^2 equivalent to 36. 
(-6)^2 = 36 = b^2 = 4ac

The Hence   option C = -6    is the answer with only ONE unique solution.

All other options have two unique solutions.

generis · Answer

The expression b^2 - 4ac is the "discriminant" of the quadratic equation. If b^2 - 4ac > 0 , there are two solutions If b^2 - 4ac = 0 , there is one solution If b^2 - 4ac < 0 , there are no solutions There are two unique solutions here so b^2 - 4ac > 0 a = 1 c = 9 4ac = 36 b^2 - 36 > 0 b^2 > 36 \sqrt{b^2} > \sqrt{36} b > 6 and b < -6 Option C violates these conditions. If b = -6 , then (b^2-4ac)=((-6)^2-36)=(36-36)=0 = ONE solution ANSWER C * The other four answers work. Answers B (b = -6.5) and D (b = 6.5) yield b^2=42.25 : (42.25 - 36) = 6.25 , which is > 0. Two unique solutions. Answers A (b=10) and E (b=10) yield b^2=100 : (100 - 36) = 64 , which is > 0. Two unique solutions.

JeffTargetTestPrep · Answer

Looking at our answer choices, we see that b cannot be -6. If b were -6 we would have:

(x - 3)(x - 3) = 0

x^2 - 6x + 9 = 0

However, because there must be two unique solutions, -6 is not a possible value for b.

Answer: C

push12345 · Answer

Putting value of C in eqn
Makes eqn as (x-3)^2=0
Which is giving a unique solution

So C is answer

Posted from my mobile device

PolarisTestPrep · Answer

Hey guys

Hopefully you have enough experience with quadratic expressions to eyeball the answer here

For shorthand, in a quadratic expression  x^2 + bx + c = 0  factored as  (x + y)(x + z) = 0 , b is the result of adding y and z, and c is the result of multiplying them

That is, the middle coefficient (the number that multiplies the variable x) is the result of adding y and z, and the last number is the result of multiplying y and z

Here is an example:

x^2 - 2x + 15 = 0

The b here is -2 and the c is 15

This factors into (x + 3)(x - 5) = 0

Multiplying back out we see  x^2   - 5x + 3x  + (3 * -5) = 0

The middle coefficient -2 is formed by adding 3 and -5. They are added because they both have the same variable x

This is because they both multiply by x when multiplying the two factors together

So when you look at  x^2 + bx + 9 = 0 , you should think "what two numbers can multiply to make 9?"

Start with the simplest answers that work, 3 * 3 or -3 * -3

The factors can therefore be (x + 3)(x + 3) = 0 or (x - 3)(x - 3) = 0

Both will lead to a 9 in the c position

In the first case, b would be 6

In the second case, b would be -6

Since we see that -6 is in the answer choices, and one of the conditions is that there be two distinct answers to the equation, we know that -6 cannot be the value of b

This is because a b of -6 would mean the factors are (x - 3)(x - 3) = 0, in which case there would be only one solution to the equation x = 3

The problem states that there must be two unique solutions and therefore b cannot be -6

The answer is (C)

If there are two unique solutions to the equation x^2 + bx + 9 = 0, wh

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If there are two unique solutions to the equation x^2 + bx + 9 = 0, wh

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

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From 555 to 765: 210-point Improvement

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My Rewards