EmSAT EmSAT Mathematics 4 — Questions and Answers
Question 1: What is the quadratic formula?
- x = −b ± √(b²−4ac) / 2a (Correct answer)
- x = b ± √(b²−4ac) / 2a
- x = −b ± √(b²+4ac) / 2a
- x = −b ± √(b²−4ac) / a
Correct answer: x = −b ± √(b²−4ac) / 2a
The quadratic formula is x = [−b ± √(b²−4ac)] / 2a. It solves ax² + bx + c = 0 for x.
Question 2: Solve: x² − 5x + 6 = 0
- x = 2 or x = 3 (Correct answer)
- x = −2 or x = −3
- x = 1 or x = 6
- x = 2 or x = −3
Correct answer: x = 2 or x = 3
Factor: (x − 2)(x − 3) = 0, so x = 2 or x = 3.
Question 3: What is the discriminant of x² + 4x + 5 = 0?
- −4 (Correct answer)
- 4
- −36
- 36
Correct answer: −4
Discriminant = b² − 4ac = 4² − 4(1)(5) = 16 − 20 = −4. A negative discriminant means no real roots.
Question 4: What type of roots does a quadratic have if the discriminant is negative?
- Two equal real roots
- Two distinct real roots
- Two complex roots (Correct answer)
- One real root
Correct answer: Two complex roots
When the discriminant (b² − 4ac) is negative, the square root of a negative number gives imaginary numbers, resulting in two complex (non-real) roots.
Question 5: Expand: (x + 3)²
- x² + 9
- x² + 6x + 9 (Correct answer)
- x² + 3x + 9
- x² − 6x + 9
Correct answer: x² + 6x + 9
(x + 3)² = (x + 3)(x + 3) = x² + 3x + 3x + 9 = x² + 6x + 9. Remember the middle term 2(x)(3) = 6x.
Question 6: If the graph of y = ax² opens downward, what can you say about a?
- a > 0
- a = 0
- a < 0 (Correct answer)
- a = 1
Correct answer: a < 0
In y = ax², when a > 0 the parabola opens upward, and when a < 0 it opens downward. A negative coefficient causes the downward opening.
EmSAT EmSAT Mathematics 4
What is the quadratic formula?