The value of k for which the equation (k - 2) | vedclass

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(B) For the quadratic equation $(k-2)x^2 + 8x + k+4 = 0$ to have real and distinct roots,the discriminant $D > 0$:$D = 8^2 - 4(k-2)(k+4) > 0$$64 - 4(k

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$3$

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(B) For the quadratic equation $(k-2)x^2 + 8x + k+4 = 0$ to have real and distinct roots,the discriminant $D > 0$:$D = 8^2 - 4(k-2)(k+4) > 0$$64 - 4(k^2 + 2k - 8) > 0$$16 - (k^2 + 2k - 8) > 0$$-k^2 - 2k + 24 > 0 \Rightarrow k^2 + 2k - 24 $(k+6)(k-4) For the roots to be negative,the sum of roots $\alpha + \beta = -\frac{8}{k-2} 0$.From $\alpha + \beta 0 \Rightarrow k > 2$.From $\alpha \beta > 0$: $\frac{k+4}{k-2} > 0 \Rightarrow k 2$.Combining all conditions: $(-6 2)$ $AND$ $(k 2)$.The intersection is $2 Among the given options,only $k = 3$ satisfies $2 < k < 4$.

The value of $k$ for which the equation $(k - 2)x^2 + 8x + k + 4 = 0$ has both roots real,distinct,and negative is

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