EmSAT EmSAT Mathematics 4

Question 1

What is the quadratic formula?

Accepted Answer

x = −b ± √(b²−4ac) / 2a

Answer

The quadratic formula is x = [−b ± √(b²−4ac)] / 2a. It solves ax² + bx + c = 0 for x.

Question 2

Solve: x² − 5x + 6 = 0

Accepted Answer

x = 2 or x = 3

Answer

Factor: (x − 2)(x − 3) = 0, so x = 2 or x = 3.

Question 3

What is the discriminant of x² + 4x + 5 = 0?

Accepted Answer

−4

Answer

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?

Accepted Answer

Two complex roots

Answer

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

Accepted Answer

x² + 6x + 9

Answer

(x + 3)² = (x + 3)(x + 3) = x² + 3x + 3x + 9 = x² + 6x + 9. Remember the middle term 2(x)(3) = 6x.

EmSAT Practice Test

EmSAT Practice Test

EmSAT EmSAT Mathematics 4