Solving quadratic equations by factorisation — Practice questions

Question 1

Difficulty: ★☆☆

1

Solve the quadratic equation \(x^2 - 5x + 6 = 0\).

Your Answer:

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Question 2

Difficulty: ★☆☆

2

Solve the quadratic equation \(x^2 - 7x + 10 = 0\).

Your Answer:

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Question 3

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3

Solve the quadratic equation \(x^2 - 7x + 12 = 0\).

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Question 4

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4

Solve the quadratic equation \(x^2 - 8x - 20 = 0\).

Your Answer:

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Question 12

Difficulty: ★☆☆

12

Solve \( x^2 - 7x + 12 = 0 \)

Your Answer:

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Question 13

Difficulty: ★☆☆

13

Solve \( x^2 - 6x - 16 = 0 \)

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Question 14

Difficulty: ★☆☆

14

Solve: \(\quad x - \frac{6}{x-5} = 0\)

Your Answer:

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Question 15

Difficulty: ★☆☆

15

Solve: \(\frac{5x+1}{4} - \frac{2x-1}{2} = x^2\)

Your Answer:

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Roots of a quadratic

Difficulty: ★☆☆

404

Find the roots of the equation \( x^2 + 5x + 6 = 0 \).

Your Answer:

2

3

-3

-2

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Factorisation and valid roots: check 1

Difficulty: ★★☆

2221

Info

M4U-P1-QP-QUADRATICS-FACTORISATION-01

Maths4U Original · Short practice

For \(x^2+x-20=0\), enter the positive root.

Enter one number or fraction. Round decimals to at least six decimal places when needed.

Your Answer:

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Factorisation and valid roots: check 2

Difficulty: ★★☆

2222

Info

M4U-P1-QP-QUADRATICS-FACTORISATION-02

Maths4U Original · Short practice

For \(3x^2-8x-3=0\), enter the negative root.

Enter one number or fraction. Round decimals to at least six decimal places when needed.

Your Answer:

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Factorisation and valid roots: check 3

Difficulty: ★★☆

2223

Info

M4U-P1-QP-QUADRATICS-FACTORISATION-03

Maths4U Original · Short practice

Solve \(x(x-6)=0\). Which is the complete real solution set?

Choose one answer.

Your Answer:

\(x=6\)

\(x=0\) or \(x=6\)

\(x=-6\) or \(x=6\)

No solutions

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Factorisation and valid roots: check 4

Difficulty: ★★☆

2224

Info

M4U-P1-QP-QUADRATICS-FACTORISATION-04

Maths4U Original · Short practice

Solve \(\displaystyle \frac{x^2-9}{x-3}=0\).

Choose one answer.

Your Answer:

\(x=3\)

\(x=-3\) or \(x=3\)

\(x=-3\)

No solutions

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Factorisation and valid roots: review variant 1

Difficulty: ★★☆

2429

Info

M4U-P1-QP-VAR-QUADRATICS-FACTORISATION-01

Maths4U Original · Short practice

For \(x^2-2x-15=0\), enter the positive root.

Enter one number or fraction. Round decimals to at least six decimal places when needed.

Your Answer:

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Factorisation and valid roots: review variant 2

Difficulty: ★★☆

2430

Info

M4U-P1-QP-VAR-QUADRATICS-FACTORISATION-02

Maths4U Original · Short practice

For \(3x^2-7x-6=0\), enter the negative root.

Enter one number or fraction. Round decimals to at least six decimal places when needed.

Your Answer:

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Factorisation and valid roots: review variant 3

Difficulty: ★★☆

2431

Info

M4U-P1-QP-VAR-QUADRATICS-FACTORISATION-03

Maths4U Original · Short practice

How many distinct real roots does \(x(x+7)=0\) have?

Enter one number or fraction. Round decimals to at least six decimal places when needed.

Your Answer:

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Factorisation and valid roots: review variant 4

Difficulty: ★★☆

2432

Info

M4U-P1-QP-VAR-QUADRATICS-FACTORISATION-04

Maths4U Original · Short practice

Solve \(\displaystyle \frac{x^2-16}{x-4}=0\). Enter the admissible root.

Enter one number or fraction. Round decimals to at least six decimal places when needed.

Your Answer:

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\(x^2 - 5x + 6 = 0\)	Write the quadratic equation in standard form.
\(-2 \times -3 = +6\), \(-2 + -3 = -5\)	Find two numbers that multiply to give \(+6\) and add to give \(-5\).
\((x - 2)(x - 3) = 0\)	Factorise the quadratic.
\(x - 2 = 0 \quad\) or \(\quad x - 3 = 0\)	Set each factor equal to zero.
\(x = 2\) or \(x = 3\)	Final Answer.

Practice — Quadratics • Solving quadratic equations by factorisation

Question 1

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Question 2

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Question 3

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Question 4

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Question 12

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Question 13

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Question 14

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Question 15

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Roots of a quadratic

Solution:

Factorisation and valid roots: check 1

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Factorisation and valid roots: check 2

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Factorisation and valid roots: check 3

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Factorisation and valid roots: check 4

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Factorisation and valid roots: review variant 1

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Factorisation and valid roots: review variant 2

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Factorisation and valid roots: review variant 3

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Factorisation and valid roots: review variant 4

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