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OCR GCSE Maths Quadratic equations

Quadratic equations

This page covers the following topics:

1. Solving quadratics
2. Completing the square
3. The quadratic formula

Quadratics can be solved by equating one side of the equation to zero and factorising. For a product to be equal to zero, one or both of the factors must be equal to zero. Therefore, the quadratic equation can be solved by equating each factor to zero and solving for the variable.

Solving quadratics

Quadratic equations that cannot be factorised can be solved by completing the square. Completing the square results in a square plus a term, which can be solved by moving the additional term to the other side of the equation and square rooting both sides.

Completing the square

A common method to solve quadratics is by using the quadratic formula. Substituting coefficients a, b, c of the quadratic equation into the formula gives its solutions.

The quadratic formula

1

Solve xΒ² + 10x βˆ’ 24 = 0 for x by completing the square.

Solve xΒ² + 10x βˆ’ 24 = 0 for x by completing the square.

2

The area of some trapezium has an expression of 10xΒ² + 4x. Given that the area of this trapezium is 6 unitsΒ², find the positive value for x using the quadratic formula.

The area of some trapezium has an expression of 10xΒ² + 4x. Given that the area of this trapezium is 6 unitsΒ², find the positive value for x using the quadratic formula.

3

Use the quadratic formula to obtain x for 4(xΒ² + 6) βˆ’ (x βˆ’ 1) = 24(xΒ² + 1).

Use the quadratic formula to obtain x for 4(xΒ² + 6) βˆ’ (x βˆ’ 1) = 24(xΒ² + 1).

4

Solve 8xΒ² βˆ’ 2x + 21 = 13 βˆ’ 22x using the quadratic formula.

Solve 8xΒ² βˆ’ 2x + 21 = 13 βˆ’ 22x using the quadratic formula.

5

Give expression y = xΒ² βˆ’ 16x + 35 in the form of y = (x + a)Β² + b.

Give expression y = xΒ² βˆ’ 16x + 35 in the form of y = (x + a)Β² + b.

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