Question

For what value of m will x^2+mx-(m^2+m-32)=0 have equal roots

Answer 1

roots of x² + mx -( m² +m -32) = 0 are equals

it means D = b² -4ac = 0
m² - 4( m² +m -32) = 0
m² -4m² -4m +128 = 0
-3m² -4m +128 = 0
3m² + 4m -128 = 0

use quadratic formula ,

m = { -4 ±√(16 +12×128) }/6

= { -4 ± 4√97}/6

= { -2±2√97}/3

Answer 2

for a quadratic equation to have equal roots ...discriminant should be equal to zero

b²-4ac=0

m²-4(m²+m-32)=0

-3m²-4m+128=0

3m²+4m-128=0

we know that m=-4±√(16+1536)/6

=-4±√1552/6

=-2±2√97/3
I hope this will help u :)