Find the values of k for which the quadratic equation 2x^2 − (k + 2)x + k = 0 has real and equal roots.
Accepted Solution
A:
Answer:k = 2Step-by-step explanation:If the roots are real and equal then the condition for the discriminant isb² - 4ac = 0For 2x² - (k + 2)x + k = 0 ← in standard formwith a = 2, b = - (k + 2) and c = k, then(- (k + 2))² - (4 × 2 × k ) = 0k² + 4k + 4 - 8k = 0k² - 4k + 4 = 0(k - 2)² = 0Equate factor to zero and solve for k(k - 2)² = 0 ⇒ k - 2 = 0 ⇒ k = 2