Complex Numbers And Quadratic Equations

Question
CBSEENMA11015666

If one root of the equation x2+px+12 =0 is 4, while the equation x2 +px +q = 0 has equal roots, then the value of 'q' is

  • 49/3

  • 4

  • 3

  • 12

Solution

A.

49/3

Since 4 is one of the roots of equation x2 + px + 12 = 0. So it must satisfied the equation.
∴ 16 + 4p + 12 = 0
⇒ 4p = -28
⇒ p = -7
The other equation is x2 - 7x + q = 0 whose roots are equal. Let roots are α and α of above equation
therefore space sum space of space roots space equals straight alpha space plus straight alpha space equals 7 over 1
⇒ 2α = 7 ⇒ α = 7/ 2 and product of roots α.α = q ⇒ α2 = q

(7/2)2 = q
q =49/4

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