Quadratic Formula

Question 1

What does a, b and c represent in the Quadratic Formula

Answer 1

In the quadratic equation

ax² + bx + c = 0

a is the coefficient of x²

b is the coefficient of x

c is the constant

Question 2

What does it mean that x = 1 and x = 2 are the solutions of the equation

x² - 3x + 2 = 0

Answer 2

When you replace x = -1 into the equation

(-1)² - 3(-1) + 2 = 0

When you replace x = -2 into the equation

(-2)² - 3(-2) + 2 = 0

In both cases the Left hand side and Right Hand side is the same

Hence x = 1 and x = 2 is called the solution

Question 3

Is x = 1 and x = 2 the solutions of the equation

x² - 3x + 2 = 2 (or any number other than 0)

Answer 3

When you replace x = -1 into the equation

(-1)² - 3(-1) + 2 = 0

When you replace x = -2 into the equation

(-2)² - 3(-2) + 2 = 0

In both cases the LHS = 0 but the RHS = 2

Hence x = 1 and x = 2 is not the solution

It is important that the RHS = 0

Question 4

Identify the a, b and c for the equation

x² + 5x + 6 = 0

Answer 4

a = 1

b = 5

c = 6

Question 5

Identify the a, b and c for the equation

x² - 5x + 6 = 0

Answer 5

a = 1

b = -5

c = 6

Question 6

Identify the a, b and c for the equation

x² - 5x - 6 = 0

Answer 6

a = 1

b = -5

c = -6

Question 7

Identify the a, b and c for the equation

x² - 5x - 6 = 2

Answer 7

Need to change

x² - 5x - 6 = 2 to

x² - 5x - 6 - 2 = 0

x² - 5x - 8 = 0

a = 1

b = -5

c = -8

Question 8

Identify the a, b and c for the equation

x² - 5x = 0

Answer 8

a = 1

b = -5

c = 0

Question 9

Identify the a, b and c for the equation

x² + 6 = 0

Answer 9

a = 1

b = 0

c = 6

Question 10

Identify the a, b and c for the equation

x² + 6 = 2x

Answer 10

Need to change

x² + 6 = 2x to

x² - 2x + 6 = 0

a = 1

b = -2

c = 6

Question 11

Identify the a, b and c for the equation

x² + 6 - 5x = 0

Answer 11

Rearrange to

x² -5x + 6 =0

a = 1

b = -5

c = 6