Previous Year Maths Question of Chapter Polynomials (Class X)

 

Previous Year Mathematics Questions of Class 10 Chapter {Polynomials} for Examination 2023

One mark Questions

1.       If α and β are the zeroes of the quadratic polynomial 2x² – 13x + 6, then α + β= ………………                (CBSE 2020)

2.       The maximum number of zeroes a cubic polynomial can have is ……………                                        (CBSE 2020)

3.       The Zeroes of the polynomial x² – 3x – m(m + 3) are ……………….                                                      (CBSE 2020)

4.       If one zero of the quadratic polynomial x² – 5x – 6 is 6 then find the other zero.

5.       Find the zeroes of polynomial √3 x² – 8x + 4√3

6.       If the graph of a polynomial intersects x – axis at exactly two points is it necessarily a quadratic polynomials.

7.       Find the quadratic polynomial whose zeroes are -3 and -5.

Two mark Questions

1.       A teacher asked 10 of his students to write a polynomial in one variable on a paper and then to handover the paper. The following were answers given by the students: 2x + 3,   3x² + 7x + 2 ,  4x³ + 3x² + 2 , 5x³ – 7x + 2,  2x² + 3 ,  5x – ½ ,  ax³ + bx² + cx + d ,   

Answer the following questions: 

(i) How many of the above ten, are not polynomials?                     (CBSE 2020)

(ii) How many of the above ten, are quadratic polynomials?

2.       Divide (2x² – x + 3) by (2 – x) and write the quotient and the remainder.                                           (CBSE 2020)

3.     If  α and β are the zeroes of the quadratic polynomial f(x) = 5x² - 7x + 1, find the value of  α/β + α/β  .             (CBSE 2020)

4.       If one of the zeroes of the quadratic polynomial p(x) = 4x² – 8kx – 9 is equal in magnitude but opposite in sign. Of the other, find the value of K.

5.       If one root of polynomial p(x) = 5x² + 13x + m is reciprocal of other, then find the value of m.

6.       For what value of h is the polynomial f(x) = 2x³ – hx² + 5x + 9, exactly divisibility by (x + 2).

Three mark Questions

1.       Find the quadratic polynomial, the sum of product of whose zeroes are -3 and 2 respectively. Hence find the zeroes.          (CBSE 2020)

2.       For what value of k is the polynomial f(x) = 3x⁴ – 9x³ + x² + 15x + k completely divisible by 3x² – 5?            (CBSE 2019)

3.       Find the zeroes of the quadratic polynomial 7y² – 11/3 y – 2/3 and verify th relationship between the zeroes and the coefficients.            (CBSE 2019)

4.       What must be added to the polynomial P(x) = x⁴ + 2x³ – 2x² + x – 1 so that the resulting polynomial is exactly divisible by x² + 2x – 3 ?

5.       If the polynomial 6x⁴ + 8x³ + 17x² + 21x + 7 is divided by another polynomial 3x² + 4x + 1, the remainder comes out to be ax + b, find a and b.

Four mark Questions

1.       Find the zeroes of the polynomial f(x) = x³ – 5x² – 2x + 24 if it is given that the product of its two zeroes is 12.

2.       If x² + x – 12 divides p(x) = x³ + ax² + bx – 84 exactly, find a and b.