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Question

Find the nature of the roots of the following quadratic equation. If roots are real, find them
2x29x+9=0

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Solution

We have,

2x29x+9=0

Comparing that,

ax2+bx+c=0

Then,a=2,b=9,c=9

We know that,

Nature of roots are

D=b24ac

=(9)24×2×9

=8172

=9>0

Roots are real.

Find them,

2x29x+9=0

2x2(6+3)x+9=0

2x26x3x+9=0

2x(x3)3(x3)=0

(x3)(2x3)=0

If x3=0 then, x=3

If 2x3=0 then, x=32

Hence, x=3,32 is the answer.


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