GMAT Club Tests | Re: D01-41

Official Solution:

The equation\(x^2 + ax - b = 0\) has equal roots, and one of the roots of the equation\(x^2 + ax + 15 = 0\) is 3. What is the value of b?

A.\(-\frac{1}{64}\)
B.\(-\frac{1}{16}\)
C.\(-15\)
D.\(-16\)
E.\(-64\)


Since one of the roots of the equation\(x^2 + ax + 15 = 0\) is 3, then substituting we'll get:\(3^2+3a+15=0\) . Solving for\(a\) gives\(a=-8\) .

Substitute\(a=-8\) in the first equation:\(x^2-8x-b=0\) .

Now, we know that it has equal roots thus its discriminant must equal to zero:\(d=(-8)^2+4b=0\)