Question

Check whether the following equation is a quadratic
equation or not. If it is a quadratic equation find the
discriminant and write the nature of roots.
(2x+3) (3x-2) = 0

Answer 1

Answer:

Yes it is the quadratic equation.

Nature of roots:real and unequal.

Step-by-step explanation:

(2x+3)(3x-2)=0

so, 2x(3x-2)+3(3x-2)=0

6x²-4x+9x-6=0

6x²+5x-6=0

so it is in the form of ax²+bx+c hence it is a quadratic equation.

therefore,

a=6,b=5 and c=-6

Discriminant=b²-4ac

=(5)²-4(6)(-6)

=25+144

=169

so, b²-4ac>0

therefore,roots are real and unequal.

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