Q15 of 108 Page 46

If α and β are the zeroes of the quadratic polynomial f(x) = x2 – px + q then find the values of the following:

(i) α2 + β2 (ii)


When we compare the above quadratic equation with the generalized one we get,

ax2 + bx + c = 0


∴ a = 1


b = -p


c = q


Sum of zeroes = -b / a


= - (-p) / 1


α + β = p


Product of zeroes = c / a


= q / 1


αβ = q


(i) α2 + β2


(α + β) 2 = α2 + β2 + 2αβ


α2 + β2 = (α + β) 2 - 2αβ


= (p) 2 – 2q


= p2 – 2q


(ii)




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