Question

If the roots of the equation x²+px+7=0 are denoted by α and β, and α²+β²=22 , find the possible values of p

Answer 1

p = +6


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Answer 2

Answer:

The given eqn is,

x^2+px+7=0

sum of the roots = - b/ a

product of the roots = c/a

here a = 1 , b = p , c = 7

sum of the roots (alpha + beta ) = - p

product of the roots (alpha× beta ) = 7

( alpha + beta )^2 = p^2

Also given :

alpha^2 + beta^2 =22

Consider

( alpha + beta ) ^2 = p ^2

alpha^2 + 2 × ( alpha × beta ) + beta ^2 = p^2

alpha^2 + beta ^2 + 2× ( alpha × beta) = p^2

22+ 2×7 = p^2

22+14 = p^2

36 = p^2

p = + or - 6

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