Question

Find alpha, k , beta if the equation has equal roots ,

(K-4)x^{​​​​​​2} + 2(k-4)x+4=0.

Answer 1

(k-4)x²+2(k-4)x+4=0

IF BOTH THE ROOTS ARE EQUAL;THEN DISCRIMINANT ⇒b²=4ac

then a=k-4; b=2(k-4) ;c=4;

substituting the values

(2k-8)²=4×(k-4)×4

4k²+64-32k=16k-64

4k²-48k+128=0

k²-12k+32=0

(k-8)(k-4)=0

k=8,4

alpha +beta=12

alpha*beta=32

on solving these

when beta=4,alpha =8
when beta=8,alpha=4