Question

Use the discriminant to determine the number of real roots the equation has. 7x2 + 3x + 1 =0.​

Answer 1

SOLUTION

Given,

${7x}^{2} + 3x + 1 = 0$

Compare it with Ax²+ Bx+C=0, then we get

A= 7, B= 3, C= 1

The expression D= b²-4ac is called discriminant.

If b²-4ac= D≥0, then roots are real.

So,

b²-4ac

=) (3)² - 4(7)(1)

=) 9-28≥0

=) -19[13<0]

So, it is negative form.

Hope it helps ☺️

Answer 2

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,