Question

answer please ..,,,,,............

Answer 1

if a quadratic equation Ax² + Bx + C = 0 has equal roots then B² - 4AC = 0

in the above question we can notice that B = -a , A = 1 , C = a + 2

substituting the above values in B² - 4AC = 0 we get

⇒ a² - 4 × (a + 2) = 0

⇒ a² - 4a - 8 = 0

The above quadratic equation a² - 4a - 8 = 0 does not have simple integers as roots.

we know that for a quadratic equation Ax² + Bx + C = 0, the roots are

{-B (+ and -) root of (B² - 4AC)}/2A

we can notice from the equation that A = 1 and B = -4 and C = -8

substituting we get

⇒ {4 (+ and -) root of (16 - 4 × 1 × -8)}/2

⇒ {4 (+ and -) root of (16 +32)}/2

⇒ {4 (+ and -) root of (48)}/2

⇒ {2 (+ and -) 2√3}

⇒ the values of a which satisfy the quadratic equation x² - ax + a + 2 = 0 are :

a = 2 + 2√3  and a = 2 - 2√3