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  4. If the quadratic equation a x2+b x+6=0 does not have two distinct real roots, then the least value of Za + b is -

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Q. If the quadratic equation $a x^2+b x+6=0$ does not have two distinct real roots, then the least value of $Za + b$ is -

Complex Numbers and Quadratic Equations

Solution:

Put $x=0$
we get $f( x )=f(0)>6$
graph is shown as
$\Rightarrow f(2) \geq 0$
$4 a +2 b +6 \geq 0$
$2 a + b \geq-3 $
$\Rightarrow \text { least value }=-3$
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