What is the nature of the roots of the quadratic equation 4/3 x^2 - 2x + 3/4 = 0 ?

Question

What is the nature of the roots of the quadratic equation \(\frac 43 x^2 - 2x + \frac 34 = 0\)?

(A) Real and unequal

(B) Real and equal

(C) Not real

(D) None of these

Answer 1

Correct option is (B) Real and equal

The given quadratic equation is

\(\frac{4}{3} x^{2}-2 x+\frac{3}{4}=0\)

Here,

\(a=\frac{4}{3} , b=-2 \text { and } c=\frac{3}{4}\)

\(D =b^{2}-4 a c\)

\(=(-2)^{2}-4 \times \frac{4}{3} \times \frac{3}{4}\)

\(=4-4\)

\(=0\)

\(P =0\)

Hence, the equation has real and equal roots.