**Class 10**^{th} Maths

Sample Paper for Polynomials

**1.** For what value of k, (–4) is a zero of the polynomial x^{2} – x – (2k + 2)?

**2.** For what value of p, (–4) is a zero of the polynomial x^{2} – 2x – (7p + 3)?

**3.** If 1 is a zero of the polynomial p(x) = ax^{2} – 3(a – 1) x – 1, then find the value of a.

**4.** If (x + a) is a factor of 2x^{2} + 2ax + 5x + 10 find a.

**5.** Write the zeroes of the polynomial x^{2} + 2x + 1.

**6.** Write the zeroes of the polynomial x^{2} – x – 6.

**7.** Write a quadratic polynomial, the sum and product of whose zeroes are 3 and –2 respectively.

**8.** Write the number of zeroes of the polynomial y = f(x) whose graph is given in the figure.

**9.** The graph of y = f(x) is given in figure. How many zeroes are there of f(x)?

**10.** The graph of y = f(x) is given in the figure. What is the number of zeroes of f(x)?

**11.** What is the number of zeroes of the polynomial y = p(x)?

**12.** Find the zeroes of the quadratic polynomial 6x^{2} – 3 – 7x and verify the relationship between the zeroes and the coefficient of the polynomial.

**13.** Find the zeroes of the quadratic polynomial 5x^{2} – 4 – 8x and verify the relationship between the zeroes and the coefficient of the polynomial.

**14.** Find the quadratic polynomial, the sum of whose zeroes is 8 and their product is 12. Hence, find the zeroes of the polynomial.

**15.** If one zero of the polynomial (a^{2} – 9) x^{2} + 13x + 6a is reciprocal of the other, find the value of ‘a’.

**16.** If the product of zeroes of the polynomial ax^{2} – 6x – 6 is 4, find the value of ‘a’.

**17.** Find all the zeros of the polynomial x^{4} + x^{3} – 34x^{2} – 4x + 120, if two of its zeroes are 2 and – 2.

**18.** Find all the zeroes of the polynomial 2x

^{4} + 7x – 19x

^{2} – 14x + 30, if two of its zeroes are

**19.** Find the quadratic polynomial whose zeroes are 1 and –3. Verify the relation between the coefficients and the zeroes of the polynomial.

**20.** Find the zeroes of the quadratic polynomial 4x^{2} – 4x – 3 and verify the relation between the zeroes and its coefficients.

**21.** Obtain all other zeroes of the polynomial 2x

^{3} – 4x – x

^{2} + 2, if two of its zeroes are

**22.** Find all the zeroes of x4 – 3x

^{3} + 6x – 4, if two of its zeroes are

**23.** Find a quadratic polynomial whose zeroes are –4 and 3 and verify the relationship between the zeroes and the coefficients.

**24.** Using division algorithm, find the quotient and remainder on dividing f(x) by g(x), where f(x) = 6x^{3} + 13x^{2} + x – 2 and g(x) = 2x + 1

**25.** If the polynomial 6x4 + 8x^{3} + 17x^{2} + 21x + 7 is divided by another polynomial 3x^{2} + 4x + 1 then the remainder comes out to be ax + b, find ‘a’ and ‘b’

**26.** If the polynomial x^{4} + 2x^{3} + 8x^{2} + 12x + 18 is divided by another polynomial x^{2} + 5, the remainder comes out to be px + q. Find the value of p and q.

**27.** Find all the zeroes of the polynomial x

^{3} + 3x

^{2} – 2x – 6, if two of its zeroes are –

**28.** Find all the zeroes of the polynomial 2x

^{3} + x

^{2} – 6x – 3, if two of its zeroes are –

**29.** If α and β are zeroes of the quadratic polynomial x^{2} – 6x + a; find the value of ‘a’ if 3α + 2β = 20.