The value of k, so that the equation $x^{2} + x - 12 = 0$ and ${k x}^{2} + 10 x + 3 = 0$ may have one root in common which is positive is $\frac{- a}{b}$ .Find $a + b$

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Solution

roots of the equation $x^{2} + 4 x - 12 = 0$ are $- 4$ and $3$
Since, $3$ is the common root of $k x^{2} + 10 x + 3 = 0$
Therefore, $9 k + 30 + 3 = 0$
$\Rightarrow k = \frac{- 11}{3}$
$\Rightarrow a + b = 14$
Ans: 14

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