The value of k for which the quadratic equati | vedclass

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(C) The given quadratic equation is $k{x^2} + 1 = kx + 3x - 11{x^2}$.Rearranging the terms to the standard form $ax^2 + bx + c = 0$,we get:$(k + 11)x^

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$5, - 7$

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(C) The given quadratic equation is $k{x^2} + 1 = kx + 3x - 11{x^2}$.Rearranging the terms to the standard form $ax^2 + bx + c = 0$,we get:$(k + 11)x^2 - (k + 3)x + 1 = 0$.For a quadratic equation to have real and equal roots,the discriminant $D = b^2 - 4ac$ must be equal to $0$.Here,$a = (k + 11)$,$b = -(k + 3)$,and $c = 1$.Substituting these values into $D = 0$:$(-(k + 3))^2 - 4(k + 11)(1) = 0$$(k^2 + 6k + 9) - 4k - 44 = 0$$k^2 + 2k - 35 = 0$Factoring the quadratic equation:$k^2 + 7k - 5k - 35 = 0$$k(k + 7) - 5(k + 7) = 0$$(k - 5)(k + 7) = 0$Thus,$k = 5$ or $k = -7$.

The value of $k$ for which the quadratic equation $(k + 11)x^2 - (k + 3)x + 1 = 0$ has real and equal roots is:

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