Question

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

Answer 1

Answer:

Step-by-step explanation:

Let p ( x ) = x² + x - 4 = 0

Given that α and β are the roots of p ( x ).

Comparing p ( x ) with 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.