If f(x) = ax^2 + 2bx + c = 0 has imaginary ro | vedclass

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Question

(B) Let $f(x) = ax^2 + 2bx + c$. Given that $f(x) = 0$ has imaginary roots,the parabola $y = f(x)$ does not intersect the $x$-axis. This means $f(x)$

Vedclass · Accepted Answer

$c < 0$

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(B) Let $f(x) = ax^2 + 2bx + c$. Given that $f(x) = 0$ has imaginary roots,the parabola $y = f(x)$ does not intersect the $x$-axis. This means $f(x)$ is either always positive $(a > 0)$ or always negative $(a We are given $4a + 4b + c Note that $f(2) = a(2)^2 + 2b(2) + c = 4a + 4b + c$. Since $f(2) Therefore,the $y$-intercept $f(0) = c$ must also be negative. Thus,$c < 0$.

If $f(x) = ax^2 + 2bx + c = 0$ has imaginary roots and $4a + 4b + c < 0$,then:

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