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Question

The quadratic equation whose roots are three times the roots of the equation 2x2+3x+5=0, is

A
2x2+9x+45=0
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B
2x2+9x45=0
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C
5x2+9x+45=0
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D
2x29x+45=0
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E
2x2+9x+49=0
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Solution

The correct option is B 5x2+9x+45=0
Let the roots of the given equation 2x2+3x+5=0 be α and β.

Then, α+β=32 and αβ=52

Let the roots of required equation be α and β.

It is given that,

α=3α and β=3β

Now, α+β=3α+3β

=3(α+β)

=3(32)=92

Also, αβ=(3α)(3β)=9αβ

=9(52)=452

Hence, required equation is

x2(92)x+452=0

2x2+9x+45=0

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