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Question

If $$p,q,r \in R$$ and the quadratic equation $$p{x^2} + qx + r = 0$$ has no real root, then


Solution

Given that,

$$p{{x}^{2}}+qx+r=0$$    $$p,q,r$$$$\in R$$

We know that if a quadratic equation has no real root then,

$$ D<0 $$

$$ {{B}^{2}}-4AC=0 $$

$$ \Rightarrow {{q}^{2}}-4pr<0 $$

$$\Rightarrow {{q}^{2}}<4pr$$


Mathematics

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