Question

Which of the following quadratic equations has real roots?

A) 4x2 - 7x + 5 = 0 B) 5x2 - 11x + 7 = 0 C) 5x2 - 11x + 8 = 0 D) 2x2 - 7x + 5 = 0

Answer 1

Answer:

$D)2 {x}^{2} - 7x + 5 = 0$

Step-by-step explanation:

In a quadratic equation $a {x}^{2} + bx + c = 0$,

If ${b}^{2} -4 ac > 0$, The equation has real roots.

A) a = 4, b = -7, c = 5

$49 - 80 = - 31 < 0$

This equation does not have real roots

B) a = 5, b = -11, c = 7

$121 - 140 = - 19 < 0$

This equation does not have real roots

C) a = 5, b = -11, c = 8

$121 - 160 = - 39 < 0$

This equation does not have real roots

D) a = 2, b = -7, c = 5

$49 - 40 = 9 > 0$

This equation has real roots