Polynomials

Exercise 1

1. The graphs of y=p(x) are given to us, for some polynomials p(x). Find the number of zeroes of p(x), in each case.

Exercise 2

2. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeros and the coefficients.

(i) x2-2x-8

(ii) 4s2-4s+1

(iii) 6x2-3-7x

(iv) 4u2+8u

(v) t2-15

(vi) 3x2-x-4

3. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

Exercise 3

4. Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following.

(i) p(x) = x3-3x2+5x-3, g(x) = x2-2

(ii) p(x) = x4-3x2+4x+5, g(x) = x2-x+1

(iii) p(x) = x4-5x+6, g(x) = 2-x2

5. Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial.

(i) t2-3, 2t4+3t3-2t2-9t-12

(ii) x2+3x+1, 3x4+5x3-7x2+2x+2

(iii) x3-3x+1, x5-4x3+x2+3x+1

6. Obtain all other zeroes of (3x4+6x3-2x2-10x-5), if two of its zeroes are

7. On dividing (x3-3x2+x+2) by a polynomial g(x), the quotient and remainder were (x-2) and (-2x+4) respectively. Find g(x).


8. Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and

(i) deg p(x) = deg q(x)

(ii) deg q(x) = deg r(x)

(iii) deg r(x) = 0

Exercise 4

9. Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case:

10. Find a cubic polynomial with the sum of the product of its zeroes taken two at a time and the product of its zeroes are 2, -7, -14 respectively.

11. If the zeroes of the polynomial x3 -3x2 + x +1 are a-b, a, a+b, find a and b.

12. If the two zeroes of the polynomial x4 – 6x3 – 26x2 +138x -35 are 2 ± √3, find other zeroes.

13. If the polynomial x4 – 6x3 +16x2 – 25x +10 is divided by another polynomial x2 – 2x + k, the remainder comes out to be x +a, find k and a.

NCERT Solutions for Class 10 Maths- Polynomials

NCERT Grade 10-Polynomials-Questions

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