Question

Describe the nature of the roots for the equation 49x2 - 28x + 4 = 0.

A. two real roots
В.
one real root
C.
two complex roots
D.
one complex root

Answer 1

We conclude that 49x² - 28x + 4 = 0 has only one real root.

Thus, option B i.e. one real root is the correct option.

Explanation:

Given the equation

49x² - 28x + 4 = 0

comparing with the quadratic equation ax² + bx + c = 0 for x, where a ≠ 0,

here

a = 49, b = -28, c = 4

Determining the discriminant b²-4ac

b²-4ac = (-28)² - 4(49)(4)

= 784 - 784

= 0

It is clear that the discriminant b²-4ac is equal to zero.

i.e.

b²-4ac = 0

We know that if the discriminant b²-4ac = 0, then the quadratic equation has one real root.

Therefore, we conclude that 49x² - 28x + 4 = 0 has only one real root.

Thus, option B i.e. one real root is the correct option.