PRACTICE: Checking solutions of quadratics
Check each solution to see if it satisfies the given quadratic equation.
Feel free to use your calculator, especially for the messy fractions.
EXAMPLES:
a) x2 – 3x – 10 = 0
Is {–2, 6} the solution set?
(–2)2 – 3(–2) – 10 = 0
4 – 3(–2) – 10 = 0
4 + 6 – 10 = 0
0 = 0 Yes, –2 checks
(6)2 – 3(6) – 10 = 0
36 – 3(6) – 10 = 0
36 – 18 – 10 = 0
8  0 NO, 6 doesn’t work.
b) 10x2 + 3x – 18 = 0
3
Is x = – a solution?
2
10(−
3 2
)
2
+ 3 (−
3
2
) – 18 = 0
0 = 0 Yes, with a calculator
it checks out.
Yes, x = –
3
No, {–2, 6} is NOT the solution set.
is a solution to the given
2
equation (though not the only one).
1) 4x2 – 4x – 24 = 0
Is {–2, 3} the solution set?
2) x2 + x – 12 = 0
Is {–4, 5} the solution set?
3) 6x2 + 8x – 8 = 0
2
Is x = a solution?
3
4) 15x2 + 14x – 8 = 0
3
Is x = – a solution?
4
D. Stark 3/24/2017
Checking solutions of quadratics 1
KEY
PRACTICE: Checking solutions of quadratics
1) 4x2 – 4x – 24 = 0
Is {–2, 3} the solution set?
2) x2 + x – 12 = 0
Is {–4, 5} the solution set?
4(–2)2 – 4(–2) – 24 = 0
4(4) – 4(–2) – 24 = 0
16 + 8 – 24 = 0
0 = 0 Yes, –2 checks
(–4)2 + (–4) – 12 = 0
16 – 4 – 12 = 0
0 = 0 Yes, –4 checks
(5)2 + 5 – 12 = 0
25 + 5 – 12 = 0
18 = 0 NO, 3 doesn’t work.
4(3)2 – 4(3) – 24 = 0
4(9) – 4(3) – 24 = 0
36 – 12 – 24 = 0
0 = 0 Yes, 3 checks
No, {–4, 5} is NOT the solution set.
Yes, {–2, 3} is the solution set.
3) 6x2 + 8x – 8 = 0
2
Is x = a solution?
3
6(
𝟐 𝟐
)
𝟑
+ 8(
4) 15x2 + 14x – 8 = 0
3
Is x = – a solution?
4
𝟐
)–8=0
𝟑
15(−
0 = 0 Yes, with a calculator
it checks out.
Yes, x =
𝟐
−
is a solution to the given
𝟑
equation (though not the only one).
𝟏𝟔𝟏
𝟏𝟔
No, x = –
𝟑 𝟐
)
𝟒
+ 14(−
𝟑
𝟒
)–8=0
 0 No, it doesn’t work.
𝟑
is NOT a solution to the
𝟒
given equation.
D. Stark 3/24/2017
Checking solutions of quadratics 2