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Solve it, - Algebra - BITSAT-6

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)
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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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