Question

Describe the number and type of solution of the following equation. 6x2 − 7x − 5 = 0 Question 4 options: No solutions. One rational solution. Two rational solutions. Two irrational solutions.

Answer 1

two rational solutions!!

this is because

6x^2 -7x - 5 = 0
factorising this we get:
6x^2 +3x - 10x - 5 = 0
3x(2x+1) -5 (2x+1)
(3x-5) (2x+1) = 0

solve
3x-5 = 0
3x = 5
x = 5/3

2x+1 = 0
2x = -1
x = -1/2

Answer 2

The equation has two rational solutions

Explanation:

6x² - 7x - 5 = 0

(3x - 5)( 2x + 1) = 0

3x - 5 = 0 ⇒ 3x = 5 ⇒ x = 5/3 (rational number)

2x + 1 = 0 ⇒ 2x = -1 ⇒ x = -1/2 (rational number)

The equation has two rational solutions