Question

find the difference of the roots of equation x²-7x-9=0

Answer 1

Hi ,

compare x² - 7x - 9 = 0 with ax² + bx + c = 0 ,

a = 1 , b = - 7 , c = -9

if p and q are two roots of the quadratic equation,

sum of the roots = - b / a

p + q = - ( -7 ) / 1

p + q = 7 ------( 1 )

product of the roots = c / a

pq = -9 ----( 2 )

( p - q )² = ( p + q )² - 4pq

= 7² - 4 × ( - 9 )

= 49 + 36

= 85

Therefore ,

difference of the roots = p - q = ± √85

I hope this helps you.

:)