Answer:
k = 4.
Explanation:
For equal roots the discriminant b^2 - 4ac = 0, so for
kx² - 4x(k+1) + 8k - 7 = 0
b^2 - 4ac = (-4(k+1)^2 - 4 * k ( 8k - 7) = 0
16(k^2 + 2k + 1) - 32k^2 + 28k = 0
- 16k^2 + 60k + 16 = 0
-4k^2 + 15k + 4 = 0
4k^2 - 15k - 4 = 0
(4k + 1)(k - 4) = 0
So k = -0.25 or 4.
Check by substituting k = 4 into the original equation:
4x^2 - 4*(5)x + 32 - 7 = 0
4x^2 - 20x + 25 = 0
(2x - 5)^2 = 0 .
This has equal roots so k = 4 is a correct value.
For k = -0.25:
-0.25x^2 -4*-0.25(-0.25+1)x + 8*-0.25 - 7
-0.25x^2 - 1.25x - 9 = 0
This has complex roots:
b^2 - 4ac = (-1.25)^2 - 4 * -0.25 * -9
= -7.44 so this hasn't got equal roots.
Answer is k = 4.