Question

For what value of k , the equation kx(x-2)+6 = 0 has equal roots .​

Answer 1

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k = 6

Step-by-step explanation:

$\sf \: k {x}^{2} - 2kx + 6 = 0$

The equation has equal roots when the discriminant of the equation has value equal to zero,i.e., $\sf b^2-4ac=0$

Here, in this question:

a = k

b = -2k

c = 6

$\sf \: {b}^{2} - 4ac = 0 \\ \sf \: {( - 2k)}^{2} - 4 \times k \times 6 = 0 \\ \sf \: 4 {k}^{2} - 24k = 0 \\ \sf \: 4k(k - 6) = 0 \\ \sf \: k = 0 \: or \: k = 6$

If we substitute 0 as value of k , we will get everything as 0. So, the answer is 6.

k = 6

Answer 2

Step-by-step explanation:

kx(x-2)+6=0

kx²-2kx+6 =0

Since the equation has equal roots,

So,

a=k , b= -2k , c=6

=> b²=4ac

(-2k)²=4 (k) (6)

4k²= 4k (6)

Ans:- k=6 [ 4k and 4k will cut ]

So , Your answer is k=6.

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