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In the equation x^2−bx+c=0, . . .

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by M7MBA » Sun Dec 10, 2017 10:25 am
In the equation $$x^2−bx+c=0$$, b and c are constants. What is the value of b ?

(1) -3 is a root of the equation $$x^2−bx+c=0.$$

(2) x + 3 is a factor of $$x^2−bx+c=0.$$

The OA is E.

I don't know how to prove that E is the solution. Experts, may you help me?
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Source: — Data Sufficiency |

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by [email protected] » Sun Dec 10, 2017 12:51 pm
Hi M7MBA,

We're given the equation X^2 - B(X) + C=0 and we're told that B and C are constants. We're asked for the value of B.

1) -3 is a root of the equation X^2 - B(X) + C=0

Fact 1 gives us one of the solutions to the equation (X= -3), but until we have the other solution, there's no way to determine the values of B or C.
Fact 1 is INSUFFICIENT.

2) x + 3 is a factor of X^2 - B(X) + C=0

Fact 2 gives us one of the factors of the equation (which proves that one of the solutions to the equation is -3), but until we have the other solution, there's no way to determine the values of B or C.
Fact 2 is INSUFFICIENT.

Combined, Fact 1 and Fact 2 tell us the SAME thing (one of the solutions is -3), but we still don't have the other solution, so there's no way to determine the values of B or C.
Combined, INSUFFICIENT.

Final Answer: E

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