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  4. The largest integral value of b for which the roots of quadratic equation x2+(1-b) x+(b-5)=0 are opposite in sign, is

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Q. The largest integral value of $b$ for which the roots of quadratic equation $x^2+(1-b) x+(b-5)=0$ are opposite in sign, is

Complex Numbers and Quadratic Equations

Solution:

Let $f(x)=x^2+(1-h) x+(h-5)$
image
$\Rightarrow f (0)< 0 $
$\Rightarrow b -5< 0 \Rightarrow b < 5$
$\therefore b _{\text {Largest integer }}=0004 $