Question

What are the roots of y = x2 – 3x – 10?

–3 and –10
–2 and 5
2 and –5
3 and 10

Answer 1

- 2 and 5

Explanation:

to find the roots let y = 0 , then

x² - 3x - 10 = 0 ← in standard form

consider the factors of the constant term (- 10) which sum to give the coefficient of the x- term (- 3)

the factors are + 2 and - 5 , since

+ 2 × - 5 = - 10 and + 2 - 5 = - 3 , then

x² - 3x - 10 = 0

(x + 2)(x - 5) = 0 ← in factored form

equate each factor to zero and solve for x

x + 2 = 0 ( subtract 2 from both sides )

x = - 2

x - 5 = 0 ( add 5 to both sides )

x = 5

the roots are x = - 2 and x = 5