Question

if alpha,beta are the zeroes of the polynomial x square-px+q then find α square+β square​

Answer 1

Answer:

α² + β² = p² - 2q

Step-by-step explanation:

Sum of roots of x² - px + q is α + β = p.

Produce of roots of x² - px + q is αβ = q.

To see this, notice that since α and β are roots, we have

x² - px + q = ( x - α) ( x - β ) = x² - ( α + β ) x + αβ.

So anyway,

α² + β²

= ( α + β )² - 2αβ

= p² - 2q