Find the values of $a$ and $b$ , the sum and the product of the roots of the equation ${4 a x}^{2} + 4 b x + 3 = 0$ are $1 / 2$ and $3 / 16$ respectively.

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Solution

Given,

sum of roots $= \frac{1}{2}$

product of roots $= \frac{3}{16}$

$P (x) = x^{2} - (s u m - o f - r o o t s) x + (p r o d u c t - o f - r o o t s)$

$x^{2} - (\frac{1}{2}) x + (\frac{3}{16}) = 0$

$16 x^{2} - 8 x + 3 = 0$ ......(1)

Given, $4 a x^{2} + 4 b x + 3 = 0$ .......(2)

comparing (1) and (2), we get,

$4 a = 16 \Rightarrow a = 4$

$4 b = - 8 \Rightarrow b = - 2$

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