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Byju's Answer
Standard X
Mathematics
Distance Formula
Find alpha, k...
Question
Find alpha, k , beta if the equation has equal roots ,
(K-4)x
2
+ 2(k-4)x+4=0.
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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
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