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4
(x−4)(x−5)=0.
Class 9 · English Medium · Cambridge · Mathematics
Equations, patterns and functions
Factor quadratics and interpret roots and a vertex.
About this lesson and its coverage
Original Kidemy Class 9 progression. This level has its own text, examples and questions. Curriculum versions share the progression; complete board-specific coverage still needs specification matching and additional material.
Learn the idea
A quadratic can have two, one or no real roots. Factorisation, completing the square and the quadratic formula expose different features. Check whether the question asks for roots, an output or a turning point.
Worked example
x²−6x+8=(x−2)(x−4); roots2 and 4. Completing the square gives (x−3)²−1, with minimum−1.
- Identify the quantities and restrictions.
- Show a method with units or symbols.
- Check and explain the result.
Your written practice
Show your working on paper. Check your answer, then choose Next.
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-3
(x−4)²−3.
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-2
4−6.
Write in your own words. A guardian or teacher should review this response.
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Every real square is nonnegative, so x²+1 is positive.
State the real-number domain.
Write in your own words. A guardian or teacher should review this response.
Show model answer and explanation
x(x−5)=0 gives x=0 or 5; division by x excludes0.
Keep both solutions and explain the lost case.
Progress and browser storage
Notebook challenge, sources and further study
Apply the idea
Represent a quadratic by its factored and completed-square forms and compare their uses.
Review with a guardian or teacher
- Use the stated evidence or givens.
- Show reasoning rather than only a result.
- Review and explain one correction.
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