Question

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

• A. 1, two equal roots
• B. –1, no real roots
• C. 1, two distinct real roots
• D. –1, two distinct real roots

Answer 1

The correct option is C

1, two distinct real roots

Given equation: 3x² – 5x + 2 = 0

For a quadratic equation in standard form, ax² + bx + c = 0,

discriminant, D $=b^2-4ac$

Here, $a=3,b=-5$ and $c=2$

$\therefore$ Discriminant, $D=b^2–4ac$

$=(–5{)}^2–(4\times 3\times 2)=1>0$

Since discriminant is greater than 0, the given quadratic equation will have two distinct real roots.