AI generatedAlgebraGCSE Higher / IGCSE Extended

Quadratic formula - exact surd answers

Simplify a surd where possible and retain exact answers.

  • 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.

Identify . Substitute into the quadratic formula.Use brackets around negative values when substituting.Evaluate the discriminant and simplify the denominator.Simplify the surd and split the plus and minus branches.

Example 2

Solve the quadratic equation. Give all real roots.

Identify . Substitute into the quadratic formula.Use brackets around negative values when substituting.Evaluate the discriminant and simplify the denominator.Simplify the surd and split the plus and minus branches.

Your turn

Question 1

Solve the quadratic equation. Give all real roots.

Check answer
Identify . Substitute into the quadratic formula.Use brackets around negative values when substituting.Evaluate the discriminant and simplify the denominator.Simplify the surd and split the plus and minus branches.
Question 2

Solve the quadratic equation. Give all real roots.

Check answer
Identify . Substitute into the quadratic formula.Use brackets around negative values when substituting.Evaluate the discriminant and simplify the denominator.Simplify the surd and split the plus and minus branches.
Question 3

Solve the quadratic equation. Give all real roots.

Check answer
Identify . Substitute into the quadratic formula.Use brackets around negative values when substituting.Evaluate the discriminant and simplify the denominator.Simplify the surd and split the plus and minus branches.
Question 4

Solve the quadratic equation. Give all real roots.

Check answer
Identify . Substitute into the quadratic formula.Use brackets around negative values when substituting.Evaluate the discriminant and simplify the denominator.Simplify the surd and split the plus and minus branches.
Question 5

Solve the quadratic equation. Give all real roots.

Check answer
Identify . Substitute into the quadratic formula.Use brackets around negative values when substituting.Evaluate the discriminant and simplify the denominator.Simplify the surd and split the plus and minus branches.
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