Question

One of the roots of the equation 3x^2+7x−q=0 is −5. Find the other root and q.

Answer 1

Answer:

see explanation

Step-by-step explanation:

Since x = - 5 is a root of the equation then substituting x = - 5 into the equation allows q to be found

3(- 5)² + 7(- 5) - q = 0

75 - 35 - q = 0

40 - q = 0 ( subtract 40 from both sides )

- q = - 40 ⇒ q = 40

The equation can now be written as

3x² + 7x - 40 = 0

Factorise to find the other root

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term

product = 3 × - 40 = - 120 and sum = + 7

The factors are + 15 and - 8

Express the x- term using these factors

3x² + 15x - 8x - 40 = 0 ( factor the first/second and third/fourth terms )

3x(x + 5) - 8(x + 5) = 0 ← factor out (x + 5)

(x + 5)(3x - 8) = 0

Equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5 ← root already known

3x - 8 = 0 ⇒ x = $\frac{8}{3}$ ← the other root