Finding the discriminant
For each quadratic equation below, determine the number of solutions by using the discriminant. If there are any solutions, use
the remainder of the quadratic formula to find them.
1) x2 – x – 3 = 0
2) x2 + 2x – 8 = 0 3) x2 + 8x + 13 = 0 4) 7x2 + 5x + 2 = 0 5) 2x2 – 8y = 8 6) 8x2 – 2 = 0
2
7) x + 3x – 2 = 0 8) x2 – 8x = – 16
9) x2 + 6x + 10 = 0 10) 2x2 + 10x + 11 = 0
KEY:
1) 13; 2 solutions; x =
3) 12; 2 solutions; x =
5) 128; 2 solutions; x =
7) 17; 2 solutions; x =
9) – 4; no solution
√
√
√
√
2) 36; 2 solutions; x = –4 and x = 2
;x
4) – 31; no solution
; x
; x
6) 64; 2 solutions; x =
;x
10) 12; 2 solutions; x =
8) 0; 1 solution; x = 4
√
;x –