Quadratic Equations: Master the Art of Solving Quadratic Equations

Question 1

Use the quadratic formula to solve the equation: 2x² - 5x - 3 = 0.

Accepted Answer

x = (5 ± √37) / 4

Answer

x = (5 ± √27) / 4

Answer

x = (5 ± √17) / 4

Answer

x = (-5 ± √17) / 4

Question 2

Find the discriminant of the quadratic equation: ax² + bx + c = 0.

Accepted Answer

b² - 4ac

Answer

4ac - b²

Answer

b - 4ac

Answer

4ac + b²

Question 3

What is the nature of the roots of a quadratic equation with a negative discriminant?

Accepted Answer

Complex and conjugate

Answer

Real and distinct

Answer

Real and equal

Answer

Cannot be determined

Question 4

Solve the quadratic equation: (x - 2)(x + 3) = 0 by factoring.

Accepted Answer

x = 2 or x = -3

Answer

x = -2 or x = 3

Answer

x = 1 or x = -4

Answer

x = -1 or x = 4

Question 5

Identify the equation that represents a quadratic equation in standard form:

Accepted Answer

ax^2 + bx + c = 0, where a ≠ 0

Answer

ax + b = 0

Answer

x^2 + y^2 = z^2

Question 6

Which of the following is the standard form of a quadratic equation?

Accepted Answer

ax^2 + bx + c = 0 (where a ≠ 0)

Answer

ax + b = 0

Answer

x^2 + y^2 = z^2

Answer

a(x - h)^2 + k = 0

Question 7

In a quadratic equation of the form ax² + bx + c = 0, which factor determines whether the equation has real, complex, or equal roots?

Accepted Answer

b² - 4ac

Answer

a

Answer

c

Answer

b

Question 8

The discriminant of the equation 2x^2 - 5x + 3 = 0 is:

Accepted Answer

11

Answer

1

Answer

-1

Answer

-11

Question 9

Which of the following equations is in the standard form of a quadratic equation: ax^2 + bx + c = 0?

Accepted Answer

ax^2 + bx + c = 0

Answer

ax + b = c

Answer

x^2 + y^2 = z^2

Answer

y = mx + b

Question 10

In solving a quadratic equation using the factorisation method, which step comes first?

Accepted Answer

Find two numbers whose product equals the constant term and whose sum equals the coefficient of x.

Answer

Complete the square.

Answer

Apply the quadratic formula.

Answer

Graph the equation and locate the roots.

Question 11

The discriminant of a quadratic equation ax^2 + bx + c = 0 is given by which expression?

Accepted Answer

b^2 - 4ac

Answer

2b - 4ac

Answer

a - b - c

Answer

a^2 + b^2 + c^2

Question 12

What discriminant value indicates that a quadratic equation will have two complex roots?

Accepted Answer

Negative

Answer

Positive

Answer

Zero

Answer

Cannot be determined from the given information

Question 13

Which of the following equations represents a quadratic equation?

Accepted Answer

x^2 - 4x + 3 = 0

Answer

x + y = 5

Answer

3x^3 + 2x^2 - 5x + 1 = 0

Answer

y = 2x + 1

Question 14

What is the name given to the point on a parabola where it changes direction?

Accepted Answer

The point where the parabola reaches its maximum or minimum value

Answer

The point of intersection with the x-axis

Answer

The point of intersection with the y-axis

Answer

The point of symmetry

Question 15

The axis of symmetry of a parabola is represented by the equation:

Accepted Answer

The line x = h

Answer

The x-axis

Answer

The y-axis

Answer

The line y = k

Question 16

Find the discriminant of the quadratic equation: ax² + bx + c = 0

Accepted Answer

b² - 4ac

Answer

b² + 4ac

Answer

ac - 4b²

Answer

4ab - c²

Question 17

Which of the following is NOT a method for solving quadratic equations?

Accepted Answer

Substitution

Answer

Factorisation

Answer

Completing the square

Answer

Quadratic formula

Question 18

Which of the following is the axis of symmetry of the parabola y = x² - 4x + 5?

Accepted Answer

x = 2

Answer

x = -2

Answer

y = 2

Answer

y = -2

Question 19

Find the x-intercepts of the parabola y = -2x² + 4x - 3

Accepted Answer

x = 1 or x = 3/2

Answer

x = -1 or x = -3/2

Answer

x = 1 or x = -3/2

Answer

x = -1 or x = 3/2

Question 20

Find the value of x that satisfies the quadratic equation x^2 - 5x + 6 = 0.

Accepted Answer

x = 2, x = 3

Answer

x = -2, x = -3

Answer

x = 1, x = -6

Answer

x = -1, x = 6

Question 21

Solve the quadratic equation 2x^2 + 5x - 3 = 0 by completing the square.

Accepted Answer

x = -1/2, x = 3

Answer

x = 1, x = -1/2

Answer

x = -2, x = 1/2

Answer

x = 1/2, x = -3

Question 22

Find the discriminant of the quadratic equation ax^2 + bx + c = 0.

Accepted Answer

b^2 - 4ac

Answer

a^2 + b^2 + c^2

Answer

4a^2 + b^2 - c^2

Answer

ac - b^2

Question 23

What is the vertex of the parabola represented by the equation y = x^2 - 4x + 3?

Accepted Answer

(2, -1)

Answer

(1, -3)

Answer

(2, 1)

Answer

(-2, -1)

Question 24

Solve the following quadratic inequality: x^2 - 5x + 6 > 0.

Accepted Answer

x < 2 or x > 3

Answer

2 < x < 3

Answer

x ∈ ℝ

Answer

x < 3 or x > 2