The product of the roots of the equation 2a² - 5a + p = 10 is - 6. Find the value of p.

Question: The product of the roots of the equation 2a² - 5a + p = 10 is - 6. Find the value of p.

Solution:
Rearranging the given equation we have 2a² - 5a + (p - 10) = 0

We know that,
if ax² + bx + c = 0 is a quadratic equation, then the product of their roots = c/a

Given the product of the roots = - 6
⇒ (p - 10)/2 = - 6
⇒ (p - 10) = - 12
⇒ p = - 12 + 10
p = - 2