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Question

The value of a for which one root of the quadratic equation (a25a+3)x2+(3a1)x+2=0 is twice as large as the other, is :

A
23
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B
13
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C
13
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D
23
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Solution

The correct option is C 23
let us rewrite the equation as ax2+bx+c=0 having roots as α and 2α
2α2=ca ...(i)
And 3α=ba ...(ii)
From (i) and (ii) by elimination of α, we get
2b2=9ac
Substituting the actual values of a,b,c, we obtain
2(3a1)2=9(2)(a25a+3)
9a26a+1=9a245a+27 ...(iii)
Therefore from (iii), we have
a=23

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