Question

If 2/3 and -3 are the roots of the equation px^2+7x+q=0, find the values of p and q.

Answer 1

p = 3

q = -6

Explanation:

Work backwards from the roots:

x =
`(2)/(3)`

3x = 2

3x - 2 = 0

Other root:

x = -3

x + 3 = 0

Multiply them together:

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

3x² - 9x + 2x - 6 = 0

3x² - 7x - 6 = 0

p = 3

q = -6

Answer 2

p = 3

q = -6

Explanation:

See the image for detailed steps.