If $α, β$ are roots of the equation $x^{2} + a x + b = 0$ then Find the value of expression
$\frac{(α - β)^{2}}{4}$ will be

\sqrt{\frac{a^{2} - 4 b}{16}}

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\frac{a^{2} - 4 b}{4}

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Solution

The correct option is C $\frac{a^{2} - 4 b}{4}$
Let $α, β$ be the roots of $x^{2} + a x + b = 0$
Then,
$α + β = - a$
$α β = b$
$(α - β)^{2} = (α + β)^{2} - 4 α β$
$(α - β)^{2} = (- a)^{2} - 4 b$
$(α - β)^{2} = a^{2} - 4 b$
$(α - β)^{2} / 4 (a^{2} - 4 b) / 4$

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If α,β are roots of the equation x2+ax+b=0 then Find the value of expression(α−β)24 will be

The correct option is C a2−4b4Let α,β be the roots of x2+ax+b=0Then, α+β=−aαβ=b(α−β)2=(α+β)2−4αβ(α−β)2=(−a)2−4b(α−β)2=a2−4b(α−β)2/4(a2−4b)/4

If $α, β$ are roots of the equation $x^{2} + a x + b = 0$ then Find the value of expression
$\frac{(α - β)^{2}}{4}$ will be

The correct option is C $\frac{a^{2} - 4 b}{4}$
Let $α, β$ be the roots of $x^{2} + a x + b = 0$
Then,
$α + β = - a$
$α β = b$
$(α - β)^{2} = (α + β)^{2} - 4 α β$
$(α - β)^{2} = (- a)^{2} - 4 b$
$(α - β)^{2} = a^{2} - 4 b$
$(α - β)^{2} / 4 (a^{2} - 4 b) / 4$