Describe the nature of the roots of the equation 4x^2-3x+9/16 =0?

Question

please explain how to solve and following are answer choices.
a. 1 real root
b. 2 real roots
c. 2 imaginary roots
d. no complex roots

Thanx!

Answer 1

b^2 - 4ac = (-3)^2 - 4(4)(9/16)
= 9 - 9 = 0
since discriminant is 0, there is only one 1 real root

Answer 2

Another Method

4x² - 3x + 9/16 = 0

Multiply both sides of the equation by 16

16(4x² - 16(3x) + 16(9/16) = 16(0)

64x² - 48x + 9 = 0

the middle term is - 48x

Find the sum of the middle term

multiply the first term 64 by the last term9 equals 576 and factor

factors of 576 are

1 x 576
2 x 288
3 x 192
4 x 144
6 x 96
8 x 72
9 x 64
12 x 48
16 x 36
18 x 32
24 x 24. . .<=. .use these factors

- 24 and - 24 satisfy the sum of the middle term

Insert - 24x and - 24x into the equation

64x² - 48x + 9 = 0

64x² - 24x - 24x + 9 = 0

8x(8x - 3 - 3(8x - 3) = 0

(8x - 3)(8x - 3)

- - - - - - - - -
Roots

8x - 3 = 0

8x - 3 + 3 = 0 + 3

8x = 3

8x / 8 = 3 / 8

x = 3 / 8

- - - - - - - - -

One real root

- - - - - - - - -s-

Answer 3

1 real root because the discriminant =0 A

Answer 4

The equation may be factored to

(x - 3/8)² = 0

Take the square root of both sides:

(x - 3/8) = 0

one real root.

x = 3/8
.

Answer 5

ues b^2 - 4ac

(-3)^2 - 4(4)(9/16) = 0

therefore there is no complex roots
and there is only 1 root.