$2 a c = b^{2} + a b$ is the condition for the sum of the roots of $a x^{2} + b x + c = 0$ is equal to the sum of the squares of the roots.

True

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False

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Solution

The correct option is A True
$α + β = α^{2} + β^{2}$ (given)
$\Rightarrow (α + β) = (α + β)^{2} - 2 α β$
$\Rightarrow (- b / a) = {(\frac{- b}{a})}^{2} - 2 (\frac{c}{a})$
$\Rightarrow b^{2} - 2 a c = - a b$
$\Rightarrow b^{2} + a b = 2 a c$

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2ac=b2+ab is the condition for the sum of the roots of ax2+bx+c=0 is equal to the sum of the squares of the roots.

The correct option is A Trueα+β=α2+β2 (given)⇒(α+β)=(α+β)2−2αβ⇒(−b/a)=(−ba)2−2(ca)⇒b2−2ac=−ab⇒b2+ab=2ac

$2 a c = b^{2} + a b$ is the condition for the sum of the roots of $a x^{2} + b x + c = 0$ is equal to the sum of the squares of the roots.

The correct option is A True
$α + β = α^{2} + β^{2}$ (given)
$\Rightarrow (α + β) = (α + β)^{2} - 2 α β$
$\Rightarrow (- b / a) = {(\frac{- b}{a})}^{2} - 2 (\frac{c}{a})$
$\Rightarrow b^{2} - 2 a c = - a b$
$\Rightarrow b^{2} + a b = 2 a c$