Question

Find the value of k for which the equation Xsquare +k(2x+k-1)+2=0 has a real
And equal root

Answer 1

${x}^{2} + k(2x + k - 1) + 2 = 0 \\ ( {x}^{2} ) + (2kx) + ( {k}^{2} - k + 2) = 0 \\ a {x}^{2} + bx + c = 0$

Since the equation has equal and real roots,

b²-4ac = 0

${(2k)}^{2} - 4(1)( {k}^{2} - k + 2) = 0 \\ 4 {k}^{2} - 4 {k}^{2} + 4k - 8 = 0 \\ 4k - 8 = 0 \\ k = \frac{8}{4} = 2$

Hence, k=2

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Answer 2

Refers to attachment ♡~