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Question: If the roots of the equation 12x<sup>2</sup> + mx + 5 = 0 are in the ratio 3 : 2, then m equals –...

If the roots of the equation 12x2 + mx + 5 = 0 are in the ratio 3 : 2, then m equals –

A

1/12

B

5/12

C

± 5105\sqrt{10}

D

± 510/125\sqrt{10}/12

Answer

± 5105\sqrt{10}

Explanation

Solution

ratio is m : n then b2ac\frac{b^{2}}{ac}= (m+n)2mn\frac{(m + n)^{2}}{mn}

⇒ m260=256\frac{m^{2}}{60} = \frac{25}{6} ⇒ m = ± 5 10\sqrt{10}