(D) Let $f(x) = a x^{2} + b x + c$. Given that $f(1) = a + b + c < 0$. Since the quadratic equation $a x^{2} + b x + c = 0$ has imaginary roots,the gr

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(D) Let $f(x) = a x^{2} + b x + c$. Given that $f(1) = a + b + c Since the quadratic equation $a x^{2} + b x + c = 0$ has imaginary roots,the graph of $f(x)$ does not intersect the $x$-axis. This means $f(x)$ is either always positive $(a > 0)$ or always negative $(a Since $f(1) Also,$f(0) = c$. Since $f(x)$ is always negative,$f(0) Thus,$a < 0$ and $c < 0$.

Class 11 Mathematics 4-2.Quadratic Equations and Inequations Quadratic expressions and Position of roots

Easy

Let $a, b, c$ be real numbers such that $a+b+c < 0$ and the quadratic equation $a x^{2}+b x+c=0$ has imaginary roots. Then:

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A
$a > 0, c > 0$
B
$a > 0, c < 0$
C
$a < 0, c > 0$
D
$a < 0, c < 0$

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4-2.Quadratic Equations and Inequations

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Quadratic expressions and Position of roots

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Let $a, b, c$ be real numbers such that $a+b+c < 0$ and the quadratic equation $a x^{2}+b x+c=0$ has imaginary roots. Then:

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If $\alpha$ and $\beta$ are the roots of the quadratic equation $x^2 - 3x + a = 0$,where $a \in R$ and $\alpha < 1 < \beta$,then which of the following is true?

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