Question

if alpha and beta are the two zeros of the quadratic polynomial f(x) = x square-p x+q, Then Find the value of alpha square+beta Square

Answer 1

Heya !!!




F(X) = X² - PX + Q



sum of zeroes = -B/A




Alpha + Beta = -(-P)/1




Alpha + Beta = P -------(1)




And,




Product of zeroes = C/A




Alpha × Beta = Q --------(2)





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( Alpha)² + (Beta)²




=> ( Alpha + Beta )² - 2Alpha Beta





=> (P)² - 2 × Q





=> -2Q + P²






★ HOPE IT WILL HELP YOU ★

Answer 2

Hey!!
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p (x) = x^2 - px + q

( This is in the form of ax^2 - bx + c)

Sum of zeroes = -b/a

alpha + beta = - ( - p)/1

alpha + beta = p----------------(i)

Product of zeroes = c/a

alpha × beta = c/a

alpha × beta = q----------------(ii)

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(alpha)^2 + (beta)^2

(alpha + beta)^2 - 2 alphabeta

p^2 - 2q.
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Hope it will helps you:-)