Question

Find the value of α²+β²,if α and β are zeroes of 5x²+3x-1.

Answer 1

Answer:

$\alpha ^{2} +\beta ^{2} = 19/25$

Explanation:

$5x^2 + 3x - 1\\\\\alpha +\beta = -3/5\\\\\alpha \beta =-1/5\\\\(\alpha +\beta )^2 = (-3/5)^2\\\\\alpha ^2 + \beta ^2 + 2\alpha \beta =9/25\\\\\alpha ^2 + \beta ^2 = 9/25 - 2\alpha \beta \\\\\alpha ^{2} + \beta ^{2} = 9/25 - 2(-1/5)\\\\\alpha ^{2} + \beta ^{2} = 9/25 + 2/5 \\\\\alpha ^{2} + \beta ^{2} = (9 + 2(5))/25\\\\\alpha ^{2} + \beta ^{2} = (9 + 10)/25\\\\\alpha ^{2} + \beta ^{2} = 19/25$

Hope it is useful...