If $α, β$ are roots of $x^{2} - 3 a x + a^{2} = 0$ such that $a^{2} + b^{2} = 1.75,$ then possible values of $a$ are

$\frac{1}{2}$ , $\frac{- 1}{2}$

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1, $\frac{- 1}{2}$

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-1 , - $\frac{1}{2}$

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1, $\frac{1}{2}$

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Solution

The correct option is A
$\frac{1}{2}$ , $\frac{- 1}{2}$

Given: $α, β$ are roots of $x^{2} - 3 a x + a^{2} = 0$ such that $a^{2} + b^{2} = 1.75,$
Using the relation between roots and coefficients
$α + β = 3 a$ and
$α β = a^{2}$

Also $a^{2} + β^{2} = \frac{7}{4}$

Then using the identity $(α + β)^{2} = a^{2} + β^{2} + 2 α β$
$\Rightarrow 9 a^{2} = \frac{7}{4} + 2 a^{2}$
$\Rightarrow 7 a^{2} = \frac{7}{4}$
$\Rightarrow a = \pm \frac{1}{2}$

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If α,β are roots of x2−3ax+a2=0 such that a2+b2=1.75, then possible values of a are

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If $α, β$ are roots of $x^{2} - 3 a x + a^{2} = 0$ such that $a^{2} + b^{2} = 1.75,$ then possible values of $a$ are