wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

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

(K-4)x​​​​​​2 + 2(k-4)x+4=0.

Open in App
Solution

(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


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Distance Formula
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon