Question

if alfa and beta are the roots of equation X2+x-4=0 from the quadratic equations whose roots are alfa square and beta square ​

Answer 1

Answer:

Step-by-step explanation:

Given that, α and β are the zeroes of the quadratic polynomial x² + x - 4 = 0.

Comparing the given equatioequationwith ax²+ bx + c = 0,

We have, a = 1 , b = 1 and c = - 4.

∴x = - b ± √ b² - 4ac /2a

= - 1 ± √ ( 1 )² - 4 ( 1 ) ( - 4 ) / 2 ( 1 )

= - 1 ± √ 1 + 16 / 2

= - 1 ± √ 17 / 2

∴ α = - 1 + √ 17 / 2 and β = - 1 - √ 17 / 2.

∴ α² + β² = [ ( - 1 + √ 17 ) / 2 ]² + [ ( - 1 - √ 17) / 2 ]²

= [ ( 1 + 17 - 2√ 17 ) / 4 ] + [ ( 1 + 17 + 2√ 17 ) / 4 ]

= ( 18 - 2√ 17 ) / 4 + ( 18 + 2√ 17 ) / 4

= ( 18 - 2√ 17 + 18 + 2√ 17 ) / 4

= 36 / 4

= 9 is the answer.