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Quadratic equations

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WorksheetWise · Standard · 1097

Quadratic equations

Work through each question. Show your reasoning where space is provided.

Name: ____________________ · Date: ____________

  1. 1. Solve over the real numbers: x² + (-20)x + (99) = 0. Give every distinct root.

  2. 2. Solve over the real numbers: x² + (7)x + (-44) = 0. Give every distinct root.

  3. 3. Solve over the real numbers: x² + (-5)x + (-24) = 0. Give every distinct root.

  4. 4. Solve over the real numbers: x² + (9)x + (0) = 0. Give every distinct root.

  5. 5. Solve over the real numbers: x² + (9)x + (20) = 0. Give every distinct root.

WorksheetWise · en-gb · 1/1

WorksheetWise · Standard · 1097

Quadratic equations — Answer key

Work through each question. Show your reasoning where space is provided.

  1. 1. Solve over the real numbers: x² + (-20)x + (99) = 0. Give every distinct root.

    x = 9; x = 11

    x² + (-20)x + (99) = (x − (9))(x − (11)). Set each factor equal to zero.

  2. 2. Solve over the real numbers: x² + (7)x + (-44) = 0. Give every distinct root.

    x = 4; x = -11

    x² + (7)x + (-44) = (x − (4))(x − (-11)). Set each factor equal to zero.

  3. 3. Solve over the real numbers: x² + (-5)x + (-24) = 0. Give every distinct root.

    x = 8; x = -3

    x² + (-5)x + (-24) = (x − (8))(x − (-3)). Set each factor equal to zero.

  4. 4. Solve over the real numbers: x² + (9)x + (0) = 0. Give every distinct root.

    x = 0; x = -9

    x² + (9)x + (0) = (x − (0))(x − (-9)). Set each factor equal to zero.

  5. 5. Solve over the real numbers: x² + (9)x + (20) = 0. Give every distinct root.

    x = -4; x = -5

    x² + (9)x + (20) = (x − (-4))(x − (-5)). Set each factor equal to zero.

WorksheetWise · en-gb · 1/1

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Mathematics

Addition

Level: 0, 1, 2, 3, 4, 5, 6

Subtraction

Level: 0, 1, 2, 3, 4, 5, 6

Multiplication

Level: 2, 3, 4, 5, 6

Division

Level: 3, 4, 5, 6

Counting

Level: 0, 1

Fractions

Level: 2, 3, 4, 5, 6

Decimals

Level: 4, 5, 6

Place value

Level: 1, 2, 3, 4, 5, 6

Telling time

Level: 1, 2, 3, 4

Money

Level: 1, 2, 3, 4, 5

Geometry

Level: 1, 2, 3, 4, 5, 6

Word problems

Level: 1, 2, 3, 4, 5, 6

Phonics

Frequent words

Level: 0, 1, 2

Short words

Level: 0, 1

Word families

Level: 0, 1

Consonant blends

Level: 0, 1, 2

Letter groups

Level: 0, 1, 2

Vowel patterns

Level: 0, 1, 2

Short vowel words

Level: 0, 1

Spelling

Spelling

Level: 0, 1, 2, 3, 4, 5

Grammar

Parts of speech

Level: 1, 2, 3, 4, 5, 6

Punctuation

Level: 1, 2, 3, 4, 5, 6

Sentence structure

Level: 1, 2, 3, 4, 5, 6

Secondary mathematics

Signed integers

Level: 7, 8, 9

Ratios

Level: 7, 8, 9

Percentages

Level: 7, 8, 9

Two-step equations

Level: 7, 8, 9

Inequalities

Level: 7, 8, 9

Slope

Level: 7, 8, 9

Pythagorean theorem

Level: 7, 8, 9

Scientific notation

Level: 7, 8, 9

Science

Force, mass and acceleration

Level: 7, 8, 9, 10

Density, mass and volume

Level: 7, 8, 9, 10

Monohybrid inheritance

Level: 7, 8, 9, 10

Balancing chemical equations

Level: 7, 8, 9, 10

Accounting

The accounting equation

Level: 10, 11, 12

Gross profit and margin

Level: 10, 11, 12

Straight-line depreciation

Level: 10, 11, 12

Geography

Map scale and distance

Level: 7, 8, 9, 10

Population density

Level: 7, 8, 9, 10

Rainfall data

Level: 7, 8, 9, 10

Computing

Binary and decimal numbers

Level: 7, 8, 9, 10

Tracing algorithms

Level: 7, 8, 9, 10

Boolean logic

Level: 7, 8, 9, 10

Advanced mathematics

Quadratic equations

Level: 10, 11, 12

Polynomial differentiation

Level: 10, 11, 12

Polynomial integration

Level: 10, 11, 12

Reading

Reading: evidence and inference

Level: 6, 7, 8, 9

History

History: evaluating historical sources

Level: 6, 7, 8, 9

Practice assessments

Practice assessment · Secondary mathematics

Level: 7, 8, 9

Practice assessment · Science

Level: 7, 8, 9, 10

Practice assessment · Accounting

Level: 10, 11, 12

Practice assessment · Geography

Level: 7, 8, 9, 10

Practice assessment · Computing

Level: 7, 8, 9, 10

Practice assessment · Advanced mathematics

Level: 10, 11, 12

About these resources

WorksheetWise authors these practice questions and translations. Numerical answers are checked by automated tests. Reading and history include marking guidance. These materials have not been independently certified by an exam board.

For UK families, tutors and classrooms. A4 paper is selected initially. Use these maths activities alongside the current lesson; Year groups and expectations differ across the UK, and no national curriculum alignment is claimed.