10 questions🇬🇧English
🧮 Quadratics & the Discriminant – A-level
Maths · A-level — completing the square, using b²−4ac to count roots and solving quadratic inequalities
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Questions
What is the value of the discriminant of x² + 5x + 3?
13
22
7
37
20s
Which of these is x² − 6x + 2 written in completed-square form?
(x − 3)² − 7
(x + 3)² − 7
(x − 6)² − 34
(x − 3)² + 11
30s
A quadratic equation has b² − 4ac < 0. How many real roots does it have?
No real roots
One repeated real root
Two real roots of opposite sign
Two distinct real roots
20s
What are the coordinates of the turning point of y = (x + 4)² − 9?
(4, 9)
(−4, 9)
(−4, −9)
(4, −9)
20s
Which of these is 2x² + 12x + 5 written in completed-square form?
2(x + 3)² − 31
2(x + 3)² − 4
2(x + 6)² − 67
2(x + 3)² − 13
30s
The equation x² + kx + 9 = 0 has equal roots. What is the positive value of k?
9
6
3
36
30s
What is the solution of the inequality x² − x − 6 < 0?
−3 < x < 2
x < −3 or x > 2
−2 < x < 3
x < −2 or x > 3
30s
For which values of k does x² + 4x + k = 0 have two distinct real roots?
k > 4
k ≤ 4
k < 4
k < 16
30s
The line y = 2x + c is a tangent to the curve y = x² + 4x + 5. What is the value of c?
5
6
4
−4
60s
For which values of k does kx² + 6x + k = 0 have no real roots?
k > 3 only
k < −9 or k > 9
k < −3 or k > 3
−3 < k < 3
60s