Question

Connect each imaginary root pair to the quadratic equation it satisfies. You must test the roots algebraically to confirm each match. The quadratic equations are x=2+i, x=+2i, x=-1+3i, and x=+8i. The Imaginary root pairs are 3x^2+12=0, x^2-4x+5=0, x^2+64=0, and x^2+2x+10=0.

Answer 1

Matches (each root with its conjugate) and algebraic checks:

- x = 2 ± i → x^2 − 4x + 5 = 0
Check: (2 + i)^2 − 4(2 + i) + 5 = (3 + 4i) − 8 − 4i + 5 = 0.

- x = ±2i → 3x^2 + 12 = 0 (equivalently x^2 + 4 = 0)
Check: 3(2i)^2 + 12 = 3(−4) + 12 = −12 + 12 = 0.

- x = −1 ± 3i → x^2 + 2x + 10 = 0
Check: (−1 + 3i)^2 + 2(−1 + 3i) + 10 = (−8 − 6i) + (−2 + 6i) + 10 = 0.

- x = ±8i → x^2 + 64 = 0
Check: (8i)^2 + 64 = −64 + 64 = 0.