If one root of equation x2 + ax + 12 = 0 is 4 while the equation x2 + ax + b = 0 has equal roots, then the value of b is

# If one root of equation x2 + ax + 12 = 0 is 4 while the equation x2 + ax + b = 0 has equal roots, then the value of b is

1. A

$\frac{4}{49}$

2. B

$\frac{49}{4}$

3. C

$\frac{7}{4}$

4. D

$\frac{4}{7}$

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### Solution:

Since, 4 is a root of ${x}^{2}+ax+12=0$
$\begin{array}{l}\therefore 16+4\mathrm{a}+12=0\\ ⇒ \mathrm{a}=-7\end{array}$
Let the roots of the equation ${x}^{2}+ax+b=0$ be $\alpha$ and $\alpha$

and $\mathrm{\alpha }\cdot \mathrm{\alpha }=\mathrm{b}⇒{\left(\frac{7}{2}\right)}^{2}=\mathrm{b}$

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