Question

26. If the equation (k − 2)x^2 - (k-4)x - 2 = 0 has difference
of roots as 3, then find the value of k.

please anyone help. ​

Answer 1

Answer:

$k = 3, \frac{3}{2}$

Step-by-step explanation:

Let

$\alpha$

and

$\beta$

be the roots.

$\alpha - \beta = 3$

$\alpha + \beta = \frac{ - ( - (k - 4))}{(k - 2)} \\ = \frac{(k - 4)}{(k - 2)}$

$\alpha \beta = \frac{ - 2}{(k - 2)}$

Use the formula

${(a - b)}^{2} = {(a + b)}^{2} - 4ab$

${3}^{2} = { (\frac{(k - 4)}{(k - 2)}) }^{2} - 4( \frac{ - 2}{(k - 2)} )$

$9 {(k - 2)}^{2} = {(k - 4)}^{2} + 8(k - 2)$

$9 {k}^{2} - 36k + 36 = {k}^{2} - 8k + 16 + 8k - 16$

$8 {k}^{2} - 36k + 36 = 0$

$2 {k}^{2} - 9k + 9 = 0$

$2 {k}^{2} - 6k - 3k + 9 = 0$

$2k(k - 3) - 3(k - 3) = 0$

$(k - 3)(2k - 3) = 0$

$k = 3 , k = \frac{3}{2}$

Answer 2

Answer:

sach me joke nnhi mar rahe ho naa

Step-by-step explanation:

agar parhe ho to phir please kal bata do ge.

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