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Solving quadratics by factorising practice questions with answers

Foundation and Higher · Grade 5 · Non-calculator

A second set of solving quadratics by factorising questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.

More questions

Question 1 Easy

Solve x^2+7x+10=0.

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Answer: -5 or -2

  1. Factorise: (x+2)(x+5) = 0.
  2. Solve: x = -5 or -2.
  • Method (1): Factorise: (x+2)(x+5) = 0.
  • Accuracy (1): Solve: x = -5 or -2.

Question 2 Easy

Solve x^2+4x+3=0.

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Answer: -3 or -1

  1. Factorise: (x+1)(x+3) = 0.
  2. Solve: x = -3 or -1.
  • Method (1): Factorise: (x+1)(x+3) = 0.
  • Accuracy (1): Solve: x = -3 or -1.

Question 3 Medium

Solve x^2+4x=0.

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Answer: -4 or 0

  1. Factorise common factor: x(x+4) = 0.
  2. Solve: x = -4 or 0.
  • Method (1): Factorise common factor: x(x+4) = 0.
  • Accuracy (1): Solve: x = -4 or 0.

Question 4 Medium

Solve x^2+6x=0.

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Answer: -6 or 0

  1. Factorise common factor: x(x+6) = 0.
  2. Solve: x = -6 or 0.
  • Method (1): Factorise common factor: x(x+6) = 0.
  • Accuracy (1): Solve: x = -6 or 0.

Question 5 Hard

Solve x^2-2x-8=0 and give the positive root.

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Answer: 4

  1. Factorise: (x-4)(x+2) = 0, roots 4 and -2.
  2. Select positive root: 4.
  • Method (1): Factorise: (x-4)(x+2) = 0, roots 4 and -2.
  • Accuracy (1): Select positive root: 4.

Question 6 Hard

Solve x^2-3x-10=0 and give the positive root.

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Answer: 5

  1. Factorise: (x-5)(x+2) = 0, roots 5 and -2.
  2. Select positive root: 5.
  • Method (1): Factorise: (x-5)(x+2) = 0, roots 5 and -2.
  • Accuracy (1): Select positive root: 5.

Exam-style question

A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.

Exam-style question 13 marks

Solve x^2-2x-15=0 and give the positive root.

Show answer

Answer: 5

  1. Factorise quadratic: (x-5)(x+3) = 0.
  2. Find roots: x = 5 or x = -3.
  3. Select positive root: 5.
  • Method (1): (x - 5)(x + 3) = 0
  • Accuracy (1): x = 5 and x = -3
  • Accuracy (1): 5

Quick checks

Short one-step questions. Pick an option before you open the answer.

Check 1

What does setting a factor to zero produce?

  1. A root of the equation
  2. The y-intercept
  3. The gradient
Show answer

A root of the equation If AB = 0, then A = 0 or B = 0.

Check 2

What are the roots of x^2+5x+6=0?

  1. -3 or -2
  2. 2 or 3
  3. 5 or 6
Show answer

-3 or -2 (x+2)(x+3) = 0, so x = -3 or -2.

Check 3

What are the roots of x^2-5x+6=0?

  1. 2 or 3
  2. -3 or -2
  3. -5 or 6
Show answer

2 or 3 (x-2)(x-3) = 0, so x = 2 or 3.

Check 4

What are the roots of x^2-9=0?

  1. -3 or 3
  2. 9
  3. 0 or 9
Show answer

-3 or 3 x^2 = 9, so x = -3 or 3.

Check 5

What are the roots of x^2-16=0?

  1. -4 or 4
  2. 16
  3. 0 or 16
Show answer

-4 or 4 x^2 = 16, so x = -4 or 4.

Check 6

What are the roots of x^2+4x=0?

  1. -4 or 0
  2. -4 only
  3. 0 or 4
Show answer

-4 or 0 x(x+4) = 0, so x = 0 or x = -4.

Check 7

What are the roots of x^2+6x=0?

  1. -6 or 0
  2. -6 only
  3. 0 or 6
Show answer

-6 or 0 x(x+6) = 0, so x = 0 or x = -6.

Check 8

What is the positive root of x^2-x-6=0?

  1. 3
  2. -2
  3. 6
Show answer

3 (x-3)(x+2) = 0 gives roots 3 and -2; positive is 3.

Check 9

What is the positive root of x^2-x-12=0?

  1. 4
  2. -3
  3. 12
Show answer

4 (x-4)(x+3) = 0 gives roots 4 and -3; positive is 4.

Check 10

Why is leaving brackets like (x+2)(x+3) not the final answer to solve an equation?

  1. The question asks for the values of x
  2. The signs are wrong
  3. The brackets must be expanded
Show answer

The question asks for the values of x Solving requires stating the numeric values of x.

Check 11

When does a quadratic equation have 0 as one of its roots?

  1. When there is no constant term
  2. When the constant is negative
  3. When both roots are equal
Show answer

When there is no constant term x is a common factor when c = 0: x(ax + b) = 0.

Check 12

How should two distinct roots be connected in the answer?

  1. With the word "or"
  2. With a plus sign
  3. With a multiplication sign
Show answer

With the word "or" x can take either value: root1 or root2.

Check 13

What are the roots of x^2+6x+8=0?

  1. -4 or -2
  2. 2 or 4
  3. -8 or -1
Show answer

-4 or -2 (x+2)(x+4) = 0, so x = -4 or -2.

Check 14

What are the roots of x^2+7x+10=0?

  1. -5 or -2
  2. 2 or 5
  3. -10 or -1
Show answer

-5 or -2 (x+2)(x+5) = 0, so x = -5 or -2.

Check 15

What defines a positive root?

  1. A solution greater than 0
  2. A solution with a plus sign in bracket
  3. The larger coefficient
Show answer

A solution greater than 0 Positive numbers are strictly greater than zero.

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