The interval of k for which the smaller root | vedclass

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Question

(A) Let $f(x) = x^2 + kx - 4$. For the smaller root to lie in the interval $(-1, 2)$,the function must satisfy the condition that $f(-1) > 0$ and $f(2

Vedclass · Accepted Answer

$(-\infty, -3)$

Vedclass · Answer

(A) Let $f(x) = x^2 + kx - 4$. For the smaller root to lie in the interval $(-1, 2)$,the function must satisfy the condition that $f(-1) > 0$ and $f(2) $1$. $f(-1) = (-1)^2 + k(-1) - 4 = 1 - k - 4 = -k - 3$. Since $f(-1) > 0$,we have $-k - 3 > 0$,which implies $k $2$. $f(2) = (2)^2 + k(2) - 4 = 4 + 2k - 4 = 2k$. Since $f(2) Combining both conditions $k Thus,the interval for $k$ is $(-\infty, -3)$.

The interval of $k$ for which the smaller root of the equation $x^2+kx-4=0$ lies in the interval $(-1, 2)$ is:

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