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Question: The condition for the roots of the equation, \(x^{2} + bx + c = 0,c < 0 < b,\) to be equal is....

The condition for the roots of the equation,

x2+bx+c=0,c<0<b,x^{2} + bx + c = 0,c < 0 < b, to be equal is.

A

0<α<β0 < \alpha < \beta

B

α<0<β<∣α∣\alpha < 0 < \beta < |\alpha|

C

α<β<0\alpha < \beta < 0

D

None of these

Answer

0<α<β0 < \alpha < \beta

Explanation

Solution

According to question,

2q2=9p2q^{2} = 9p

⇒ 2p2=9q2p^{2} = 9q

⇒ 9q2=2p9q^{2} = 2por x2+2mx+m2−2m+6=0x^{2} + 2mx + m^{2} - 2m + 6 = 0