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The Official Guide For GMAT® Quantitative Review, 2ND EditionIn the equation x^2 + bx + 12 = 0, x is a variable and b is a constant. What is the value of b ?
(1) x - 3 is a factor of x^2 + bx + 12
(2) 4 is a root of the equation x^2 + bx + 12 = 0
Sharing an alternate way to solve using the roots of the equation.
Let p and q be the roots of the equation, then the sum and product of the roots will be:
\(p + q\) \(=\) \(\frac{-b}{a}\) \(=\) \(-b\) (---->
1)
\(p * q\) \(=\) \(\frac{c}{a}\) \(=\) \(12\) (---->
2)
Statement-1: If \((x-3)\) is a factor then one of the roots of the equation will be \(3\). Let \(p\) \(=\) \(3\) and substitute in (---->
2)
\(3 * q\) \(=\) \(12\) therefore \(q\) \(=\) \(4\)
Substituting \( p = 3\) and \(q = 4\) in (---->
1) we get \(b = -7\)
(Sufficient)Statement-2: We are directly given that \(4\) is one of the roots. Let's assume \( q = 4 \) and substitute in (---->
2)
\(p * 4\) \(=\) \(12\) therefore \(p = 3\)
Substituting \(p = 3\) and \(q = 4 \) in (---->
1) we get \(b = -7\)
(Sufficient)Ans.
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