The value of k for which the equation 2x^2 - | vedclass

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Question

(D) The given quadratic equation is $2x^2 - (k - 1)x + 8 = 0$.For the equation to have equal and real roots,the discriminant $D$ must be equal to $0$,

Vedclass · Accepted Answer

$9$ and $-7$

Vedclass · Answer

(D) The given quadratic equation is $2x^2 - (k - 1)x + 8 = 0$.For the equation to have equal and real roots,the discriminant $D$ must be equal to $0$,where $D = b^2 - 4ac$.Here,$a = 2$,$b = -(k - 1)$,and $c = 8$.Substituting these values into the discriminant formula:$(-(k - 1))^2 - 4(2)(8) = 0$$(k - 1)^2 - 64 = 0$$(k - 1)^2 = 64$Taking the square root on both sides:$k - 1 = \pm 8$Case $1$: $k - 1 = 8 \Rightarrow k = 9$Case $2$: $k - 1 = -8 \Rightarrow k = -7$Therefore,the values of $k$ are $9$ and $-7$.

The value of $k$ for which the equation $2x^2 - kx + x + 8 = 0$ has equal and real roots is:

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