AI generatedAlgebraGCSE Higher

Solving a quadratic after rearranging

Bring all terms to one side before factorising.

  • Put the quadratic equal to zero before factorising or using the quadratic formula.
  • Keep both square-root branches. Do not divide by an expression containing , as this can remove a root.
  • Give exact answers unless rounding is requested. In a context, reject only roots that are not permitted.

Example 1

Solve the quadratic equation. Give all real roots.

Factorise the quadratic.A product is zero only when at least one factor is zero. Set each factor equal to zero and solve.
Keep this root and solve the other factor.Collect the roots in the answer.

Example 2

Solve the quadratic equation. Give all real roots.

Factorise the quadratic.A product is zero only when at least one factor is zero. Set each factor equal to zero and solve.
Keep this root and solve the other factor.Collect the roots in the answer.

Your turn

Question 1

Solve the quadratic equation. Give all real roots.

Check answer
Factorise the quadratic.A product is zero only when at least one factor is zero. Set each factor equal to zero and solve.
Keep this root and solve the other factor.Collect the roots in the answer.
Question 2

Solve the quadratic equation. Give all real roots.

Check answer
Factorise the quadratic.A product is zero only when at least one factor is zero. Set each factor equal to zero and solve.
Keep this root and solve the other factor.Collect the roots in the answer.
Question 3

Solve the quadratic equation. Give all real roots.

Check answer
Factorise the quadratic.A product is zero only when at least one factor is zero. Set each factor equal to zero and solve.
Keep this root and solve the other factor.Collect the roots in the answer.
Question 4

Solve the quadratic equation. Give all real roots.

Check answer
Factorise the quadratic.A product is zero only when at least one factor is zero. Set each factor equal to zero and solve.
Keep this root and solve the other factor.Collect the roots in the answer.
Question 5

Solve the quadratic equation. Give all real roots.

Check answer
Factorise the quadratic.A product is zero only when at least one factor is zero. Set each factor equal to zero and solve.
Keep this root and solve the other factor.Collect the roots in the answer.
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