(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 $0$.

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(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 $0$.$D = b^2 - 4ac = 0$Here,$a = 2$,$b = -(k - 1)$,and $c = 8$.Substituting these values: $(-(k - 1))^2 - 4(2)(8) = 0$$(k - 1)^2 - 64 = 0$$k^2 - 2k + 1 - 64 = 0$$k^2 - 2k - 63 = 0$Factoring the quadratic equation: $(k - 9)(k + 7) = 0$Therefore,$k = 9$ or $k = -7$.

Class 11 Mathematics 2 Complex Numbers and Quadratic Equations: Quadratic Equations Solution of quadratic equations and Nature of roots

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

A
$-9$ and $-7$
B
$9$ and $7$
C
$-9$ and $7$
D
$9$ and $-7$

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2 Complex Numbers and Quadratic Equations: Quadratic Equations

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Solution of quadratic equations and Nature of roots

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

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