If the roots of the equation $3 x^{2} + b x + 3 = 0$ are in the ratio $4 : 3$ , then find out the value of b.

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Solution

The correct option is A
Soln:

For a quadratic equation $a x^{2} + b x + C = 0$ , if the roots are in ratio $m : n$ then $m n b^{2} = (m + n)^{2} a c .$

In the equation given:

$4 \times 3 \times b^{2} = (4 + 3)^{2} (3 \times 3)$

$12 b^{2} = 49 \times 9$

$b = \frac{7 \times 3}{(2 \sqrt{3})} = \frac{7 \sqrt{3}}{2}$ Hence option (a)

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