Kx²-4x(k+1)+8k=7 has two equal roots, find the value of k

k = 4.

Step-by-step 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.

k= 7+4x/8raised to the power of 2−4x+8

Step-by-step explanation:

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answer 1 : option "c"

answer 2 : option "d"

answer 3 : option "b"

answer 4 : option "d"

answer 5 : option "b"

answer 6 : option "a"

answer 7 : option "c"

answer 8 : option "d"

answer 9 : option "c"

answer 10 : option "d"

answer 11 : option "c"

answer 12 option "b"

answer 13 option "c"

answer 14 option "c"

answer 15 option "d"

answer 16 option "a"

answer 17 option "b"

answer 18 option "c"

answer 19 option "a"

answer 20 option "a"

answer 21 option "c"

d

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step-by-step explanation: