Question

Find the discriminant of the quadratic equation $3x^2–5x+2=0$ and hence find the nature of the roots.

• A. 4, two distinct real roots
• B. –1, imaginary
• C. 1, two equal roots
• D. 1, real and distinct roots

Answer 1

The correct option is D 1, real and distinct roots

Given equation is 3x² – 5x + 2 = 0.
For the standard form of quadratic equation ax² + bx + c = 0,
discriminant is given by "$b^2-4ac$".
Here, $a=3,b=-5$ and $c=2$
$\therefore \text{Discriminant, (D)}=b^2–4ac=(–5{)}^2–(4\times 3\times 2)=1$

Since, discriminant > 0, the roots are real and distinct.