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The value of a for which one of the roots of $x^{2}-3x+2a=0$ is double of one of the roots of $x^{2}-x+a=0$ is

Option 1)
0, 2

Option 2)
0, -2

Option 3)
2, -2

Option 4)
None of these

Answers (1)

best_answer

As learnt in

Roots of Quadratic Equation with real Coefficients -

$\alpha ,\beta$ are roots if

$ax^{2}+bx+c= 0$

is satisfied by $x= \alpha ,\beta$

- wherein

$\alpha ,\beta\in C$

$a,b,c\in R$

$x^{2}-3x+2a=0$

and, $x^{2}-x+a=0$

Let first root be $2 \alpha$ , second root = $\alpha$

Thus $4\alpha^{2}-6 \alpha +2a=0$

i.e., $2\alpha^{2}-3 \alpha +a=0$

and, $\alpha^{2}- \alpha +a=0$

$-\alpha - a =0$

$\alpha= - a$

Thus, $a^{2}+a+a=0$

$a^{2}+2a=0\:\:\:\:\:\Rightarrow a=0,-2$

Option 1)

0, 2

This option is incorrect.

Option 2)

0, -2

This option is correct.

Option 3)

2, -2

This option is incorrect.

Option 4)

None of these

This option is incorrect.

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divya.saini

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