Polynomials
25 solved questions from Class 9 Mathematics, each with the full working. Tap any question to see the step-by-step solution.
- 1 Find the zeroes of the quadratic polynomial x² - 5x + 6. medium MCQ Zeroes of Polynomial
- 2 What is the degree of a non-zero constant polynomial? medium MCQ Degree of Polynomial
- 3 Solve for x: 2x + 5 = 15. medium MCQ Linear Equations
- 4 Find the discriminant (D) of x² - 4x + 4 = 0. medium MCQ Quadratic Discriminant
- 5 If the roots of ax² + bx + c = 0 are real and equal, what is D? medium MCQ Nature of Roots
- 6 Expand (a + b)². medium MCQ Algebraic Identities
- 7 Factorise x² - 9. medium MCQ Difference of Two Squares
- 8 Solve pair of equations: x + y = 10 and x - y = 4. medium MCQ Pair of Linear Equations
- 9 What is the degree of a quadratic polynomial? medium MCQ Degree of Polynomial
- 10 If x = 2 is a root of x² - kx + 10 = 0, find k. medium MCQ Roots of Equation
- 11 What is the domain, range, or fundamental theorem introduced in 'Polynomials' (Class 9 Mathematics)? medium MCQ Functions & Theorems
- 12 What is the derivative or integral formula associated with 'Polynomials'? medium MCQ Calculus & Formulae
- 13 How do you find the solution set or optimum value in 'Polynomials'? medium MCQ Problem Solving & Optimization
- 14 Find the sum of the roots of the cubic equation 5x^3-12x^2+7x-2=0. hard 4 marks Sum of roots of cubic via Viète
- 15 If x=2 is a root of the quadratic equation x^2-kx+8=0, find the value of k. medium 2 marks Using a given root to find coefficient
- 16 The quadratic equation 3x^2-12x+12=0 has equal real roots. What is the value of its discriminant? medium MCQ 3 marks Discriminant of quadratic with equal roots
- 17 Factorise the quadratic polynomial x^2-4x+3. easy 1 mark Factorisation of quadratic
- 18 Factorise the cubic polynomial x^3-3x^2+3x-1 medium 2 marks Recognising a perfect cube in a cubic
- 19 What is the product of the roots of the quadratic polynomial 2x^2+5x-12=0? easy MCQ 1 mark Product of roots of a quadratic
- 20 If x=4 is a root of the quadratic equation x^2+ax-5=0, find the value of a medium 2 marks Determining a parameter from a known root
- 21 A cubic polynomial x^3 + a x^2 + b x + c has roots 1, 2, and 3. Find the coefficients a, b, and c. hard 3 marks Coefficients from roots
- 22 For the quadratic equation 3x^2 - 10x + 4 = 0, find the sum and product of its roots. medium 2 marks Vieta’s formulas
- 23 Factorise the quadratic polynomial x^2 + 7x + 12. easy 1 mark Factoring quadratic
- 24 A cubic polynomial x^3+px^2+qx+r has roots 2, -3, and k. If the sum of the squares of the roots is 17, find all possible values of k. hard 3 marks Sum of squares of roots in a cubic
- 25 For the quadratic equation 4x^2-8x+3=0, find the sum and the product of its roots. medium 2 marks Vieta's formulas for quadratics