Worked example 1
Question: Solve x²−5x+6=0.
Solution: Factor: (x−2)(x−3)=0. Therefore x=2 or x=3. Check: each value makes the original expression zero.
What this chapter covers
Solve real quadratic equations by factorisation and the quadratic formula, use the discriminant to describe roots, and model simple situations.
Standard form and solutions
A quadratic equation has form ax²+bx+c=0 with a≠0. A solution is a value of x that makes the equation true. Factorisation is efficient when factors are visible; otherwise use the quadratic formula.
Discriminant
D=b²−4ac determines the number and type of real roots: D>0 gives two distinct real roots; D=0 gives equal real roots; D<0 gives no real roots. CBSE Class 10 questions focus on real roots.
Key formulae: x = (−b ± √(b²−4ac))/(2a); discriminant D=b²−4ac.
Worked examples: CBSE question patterns
These are original practice questions modeled on common board-exam patterns; they are not reproduced past-paper questions.
Worked example 2
Question: Find the nature of the roots of 2x²−4x+5=0.
Solution: a=2,b=−4,c=5. D=(−4)²−4(2)(5)=16−40=−24<0. Hence there are no real roots.
Practical activity / investigation
Draw a rectangle with a variable side x and fixed side 8−x. Write its area A=x(8−x), then set A=15. Factor the resulting quadratic and interpret the two possible side lengths.
Record: Write the aim, materials, steps, observations and conclusion in your notebook. Follow teacher supervision for any classroom activity.
Quick practice with answers
Try each question before opening its solution.
Practice 1: Solve x²−9x+20=0.
(x−4)(x−5)=0, so x=4 or 5.
Practice 2: For x²+4x+4=0, state the roots and their nature.
D=16−16=0; the equal roots are x=−2,−2.
Practice 3: The product of two consecutive positive integers is 72. Find them.
Let n(n+1)=72, so n²+n−72=0=(n−8)(n+9). Positive n=8; integers are 8 and 9.
Revision checklist
- Can I explain the key idea without memorising a worked solution?
- Have I selected the right formula and written units where needed?
- Can I show each algebraic or geometric step clearly?
- Can I check my answer by substitution, estimation or a diagram?
Aligned to the Class X Mathematics curriculum for 2026–27 and the NCERT Mathematics textbook. Always confirm any school-specific internal assessment with your teacher.