If the roots of the equation 3x2+bx+3=0 are in the ratio 4:

Question

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.

Options:

A . 7√32

B . √122

C . 7√3

D . 4

Answer: Option A
:
A
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}

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