The product of the roots of the equation 2x² - 5x + k = 10 is - 3. Find the value of k.

Question: The product of the roots of the equation 2x² - 5x + k = 10 is - 3. Find the value of k.

Solution:
Given,
2x² - 5x + k = 10
⇒ 2x² - 5x + (k - 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 = - 3
∴ (k - 10)/2 = - 3
⇒ k - 10 = - 6
⇒ k = - 6 + 10
∴ k = 4