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  4. If a, b, c ∈ R and quadratic equation x2+(a+b) x+c=0 has no real roots then

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Q. If $a, b, c \in R$ and quadratic equation $x^{2}+(a+b) x+c=0$ has no real roots then

Complex Numbers and Quadratic Equations

Solution:

Since $f(x)$ has no real roots, $f(x)$ has same sign for every $x$
$\therefore f(0) \cdot f(1)>0$