For what set of values of K do both roots of | vedclass

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(C) Let $f(x) = 4x^2 - 20Kx + (25K^2 + 15K - 66)$.For both roots to be less than $2$,three conditions must be satisfied:$1$. Discriminant $D \ge 0$:$D

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$(-\infty, -1)$

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(C) Let $f(x) = 4x^2 - 20Kx + (25K^2 + 15K - 66)$.For both roots to be less than $2$,three conditions must be satisfied:$1$. Discriminant $D \ge 0$:$D = (-20K)^2 - 4(4)(25K^2 + 15K - 66) = 400K^2 - 16(25K^2 + 15K - 66) = 400K^2 - 400K^2 - 240K + 1056 = -240K + 1056$.$-240K + 1056 \ge 0 \implies 240K \le 1056 \implies K \le 4.4$.$2$. Vertex $x_v $x_v = -b/(2a) = 20K / 8 = 2.5K$.$2.5K $3$. $f(2) > 0$:$f(2) = 4(2)^2 - 20K(2) + 25K^2 + 15K - 66 = 16 - 40K + 25K^2 + 15K - 66 = 25K^2 - 25K - 50 > 0$.$K^2 - K - 2 > 0 \implies (K-2)(K+1) > 0$.This implies $K > 2$ or $K Combining all conditions: $(K \le 4.4) \cap (K  2 \cup K The intersection is $K < -1$,which is $(-\infty, -1)$.

For what set of values of $K$ do both roots of the equation $4x^2 - 20Kx + (25K^2 + 15K - 66) = 0$ lie below $2$?

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