Question

if α and β are the zeroes of quadratic polynomial 2x^2-5x+8 find α^2+β^2​

Answer 1

In 2x^2 - 5x +8, a = 2, b= - 5, c= 8

Sum of zeroes (alpha +beta) = - b/a = - (-5)/2 =5/2

Product of zeroes (alpha. Beta) = c/a = 8/2 = 4

Now,

Alpha ^2 + beta ^2

(alpha +beta) ^2 - 2(alpha.beta)

(5/2) ^2 - 2 (4)

25/4 - 8

-7/4