Question

Determine the nature of roots of the equation 3x2

– 5x + 19 = 0​

Answer 1

Given:

Use the discriminant to determine the number of real roots the equation has. 3x2 – 5x + 1 =0

Solution:

Discriminant = bx2 – 4ac

Compare the above equation 3x2 – 5x + 1 =0 with ax2 + bx + c = 0

We get, a = 3, b = -5, c = 1

Put the value of a, b and c;

Discriminant = bx2 – 4ac

Discriminant = (-5)2 - 4 × 3 × 1

= 25 – 12

= 13 [13 > 0]

Therefore, discriminant is positive.

So the given equation has two distinct real roots.

Answer= Two distinct real roots,