Question

Find the roots of the quadratic equation (3x - 2)2 - 4(3x-2) + 3 = 0.​

Answer 1

Answer:

Given equation is 3x

2

−4x+3=0

To find, the nature of the roots of the equation

An equation is said to have

(i) two distinct and real roots if the discriminant b

2

−4ac>0

(ii) equal real roots if b

2

−4ac=0

(iii) no real roots or imaginary roots if b

2

−4ac<0

In the given equation a=3,b=−4,c=3

Hence the discriminant is (−4)

2

−4(3)(3)=16−36=−20<0

Therefore the roots of the given equation are imaginary in nature.