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Common Roots

If α, β are r...

Question

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

1.-1/2

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-1,-1/2

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1/2 . -1/2

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1, 1/2

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Solution

The correct option is C
1/2 . -1/2

Since α+β=3a

αβ= $a^{2}$

And $a^{2}$ + $β^{2}$ =7/4

Then $(α + β)^{2}$ = $a^{2}$ + $β^{2}$ +2αβ =>9 $a^{2}$ =7/4+2 $a^{2}$ => 7 $a^{2}$ =7/4 =>a=±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

The correct option is C 1/2 . -1/2 Since α+β=3a αβ=a2 And a2+β2=7/4 Then (α+β)2=a2+β2+2αβ =>9a2=7/4+2a2 => 7a2=7/4 =>a=±1/2

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

The correct option is C
1/2 . -1/2

Since α+β=3a

αβ= $a^{2}$

And $a^{2}$ + $β^{2}$ =7/4

Then $(α + β)^{2}$ = $a^{2}$ + $β^{2}$ +2αβ =>9 $a^{2}$ =7/4+2 $a^{2}$ => 7 $a^{2}$ =7/4 =>a=±1/2