If - 4 is a root of the equation x^2+px-4=0 and the equation x^2+px+q=0 has equal roots, find the value of p and q

p = 3, q = 2.5

Step-by-step explanation:

Given that x = - 4 is a root of the equation, then

( - 4) ² - 4p - 4 = 0, that is

16 - 4p - 4 = 0

12 - 4p = 0 (subtract 12 from both sides)

- 4p = - 12 (divide both sides by - 4)

p = 3

Also given that the equation x² + px + q = 0 has equal roots

Thus the value of the discriminant b² - 4ac = 0

Here a = 1, b = p and c = q, thus

p² - 4q = 0 ← substitute p = 3 from above into the equation

9 - 4q = 0 (subtract 9 from both sides)

- 4q = - 9 (divide both sides by - 4)

q = 2.5