Quadratic Equations

26 solved questions from Class 10 Mathematics, each with the full working. Tap any question to see the step-by-step solution.

• 1 For the quadratic 2x^2-7x+3=0, determine the nature of its roots. medium 1 mark Discriminant and nature of roots
• 2 A rectangular garden is to be designed such that its length is 5 m more than its breadth. The area of the garden must be 84 m^2. Find the dimensions of the garden. hard 3 marks Word problem – forming quadratic
• 3 Find the roots of 3x^2+2x-8=0 using the quadratic formula. medium 2 marks Quadratic formula
• 4 Solve the quadratic equation x^2-5x+6=0 by factorisation. easy 1 mark Factorisation of quadratic
• 5 For which values of m does the quadratic equation 3x^2+2mx+(m-5)=0 have real and distinct roots? medium MCQ 2 marks Discriminant >0 for real distinct roots
• 6 Without solving, state the sum and product of the roots of the quadratic equation 2x^2-7x+3=0. easy 1 mark Sum and product of roots
• 7 Without solving, find the sum of the roots of the quadratic equation 4x^2-9x+2=0. medium 2 marks Sum of roots (Vieta’s formula)
• 8 Solve the quadratic equation x^2+7x+12=0 by factorisation. easy 1 mark Factorisation of quadratics
• 9 Find the value of the parameter a for which the quadratic equation 2x^2+(a-4)x+(a-2)=0 has one root equal to 2. hard 4 marks Using a known root to find a parameter
• 10 For which values of p does the quadratic equation x^2-(2p+3)x+(p^2+3p+2)=0 have real and distinct roots? medium MCQ 2 marks Nature of roots via discriminant
• 11 Solve the quadratic equation x^2-6x+8=0 by factorisation. easy 1 mark Factorising a quadratic
• 12 Without solving, state the sum and product of the roots of the quadratic equation 3x^2-12x+9=0. easy 1 mark Sum and product of roots
• 13 A rectangular garden is to have an area of 150 m^2. Its length is 5 m more than its breadth. Find the length and breadth of the garden. medium 2 marks Word problem leading to quadratic
• 14 Find the zeroes of the quadratic polynomial x² - 5x + 6. medium MCQ Zeroes of Polynomial
• 15 What is the degree of a non-zero constant polynomial? medium MCQ Degree of Polynomial
• 16 Solve for x: 2x + 5 = 15. medium MCQ Linear Equations
• 17 Find the discriminant (D) of x² - 4x + 4 = 0. medium MCQ Quadratic Discriminant
• 18 If the roots of ax² + bx + c = 0 are real and equal, what is D? medium MCQ Nature of Roots
• 19 Expand (a + b)². medium MCQ Algebraic Identities
• 20 Factorise x² - 9. medium MCQ Difference of Two Squares
• 21 Solve pair of equations: x + y = 10 and x - y = 4. medium MCQ Pair of Linear Equations
• 22 What is the degree of a quadratic polynomial? medium MCQ Degree of Polynomial
• 23 If x = 2 is a root of x² - kx + 10 = 0, find k. medium MCQ Roots of Equation
• 24 What is the domain, range, or fundamental theorem introduced in 'Quadratic Equations' (Class 10 Mathematics)? medium MCQ Functions & Theorems
• 25 What is the derivative or integral formula associated with 'Quadratic Equations'? medium MCQ Calculus & Formulae
• 26 How do you find the solution set or optimum value in 'Quadratic Equations'? medium MCQ Problem Solving & Optimization