Amy solved the equation 2x ^ 2 + 5x - 42 = 0 She stated that the solutions to the equation were 7/2 and - 6. Do you agree with Amy's solutions? Explain why or why not.

The answer to your question is Amy is correct.

Step-by-step explanation:

Data

Equation 2x² + 5x - 42 = 0

-Factor

2 x 42 = 84

- Find the prime factors of 84

84 2

42 2

21 3

7 7

1

84 = 2² 3 7

-Find two numbers that added gives 5

These numbers are 12 and - 7

- Express the equation using these numbers

2x² + 12x - 7x - 42

-Factor by common factor

2x (x + 6) - 7 (x + 6)

-Factor by grouping

(x + 6) (2x - 7)

-Find the roots

x₁ + 6 = 0 2x₂ - 7 = 0

x₁ = - 6 2x₂ = 7

x₂ = 7/2