Question

Find the values of k for which the equation k - 4 into x square + 2 into k - 4 x + 4 is equal to zero has equal roots

Answer 1

Answer:

k = 4 or k = 8

Explanation:

Compare (k-4)x²+2(k-4)x+4=0

with ax²+bx+c=0 , we get

a = (k-4),

b = 2(k-4),

c = 4 ,

Now ,

Discreminant (D) = 0

[ Given , equal roots ]

b² - 4ac = 0

=> [2(k-4)]² -4×(k-4)×4 = 0

=> 4(k-4)² - 16(k-4) = 0

=> 4(k-4)[k-4 -4] = 0

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

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

=> k = 4 or k = 8

••••

Answer 2

(k-4)x²+2(k-4)x+4=0

a = (k-4),

b = 2(k-4),

c = 4 ,

Given , equal roots

b² - 4ac = 0

[2(k-4)]² -4×(k-4)×4 = 0

4(k-4)² - 16(k-4) = 0

4(k-4)[k-4 -4] = 0

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

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

if k = 4  we get the equation  4 =0  so it is not possible

so k= 8  is only one value to get equal roots