Question

Find the complete set of values of a for which the quadratic x²
ax + a +2=0 has equal roots.​

Answer 1

Answer:

(2 - 2√3) and (2 + 2√3)

Step-by-step explanation:

x² + px + q = 0 , if D = p² - 4q = 0 , then quadratic equation has equal roots.

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x² + ax + a + 2 = 0

p = a and q = a + 2

a² - 4(a + 2) = 0 ⇔ a² - 4a - 8 = 0

$a_{12}$ = [4 ± √(16 + 32)] / 2 = 2 ± 2√3

For a = 2 - 2√3 and a = 2 + 2√3 equation x² + ax + a + 2 = 0 has equal roots.