DPP Class 10 Polynomials

DPP Class 10 Polynomials

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DAY – 1

  1. Find the zeroes of the quadratic polynomial 6x2 – 3 – 7x and verify the relationship between the zeroes and the coefficients of the polynomial.

  2. Find the zeroes of p(x) = 2x2 – x – 6 and verify the relationship of zeroes with these co-efficients.

  3. Find the zeroes of the quadratic polynomial f(x) = x2 – 3x – 28 and verify the relationship between the zeroes and the co-efficients of the polynomial

  4. Find the zeroes of the quadratic polynomial 3x2 – 75 and verify the relationship between the zeroes and the coefficients.

  5. Find the quadratic polynomial whose zeroes are -2 and -5. Verify the relationship between zeroes and coefficients of the polynomial.

  6. Write the quadratic polynomial, whose zeroes are -4 and -5

  7. If the sum of the zeroes of the polynomial p(x) = (k2 – 14) x2 – 2x – 12 is 1, then find the value of k.

  8. If the sum of zeroes of the quadratic polynomial 3x2 – kx + 6 is 3, then find the value of k.

  9. If α and β are the zeroes of a polynomial such that α + β = -6 and αβ = 5, then find the polynomial.

  10. If α and β are the zeroes of the polynomial ax2 + bx + c, find the value of α2 + β2.

  11. If the zeroes of the polynomial x2 + px + q are double in value to the zeroes of 2x2 – 5x – 3, find the value of p and q.

  12. Form a quadratic polynomial whose zeroes are 3 + √2 and 3 – √2.

  13. If α and β are zeroes of p(x) = kx2 + 4x + 4, such that α2 + β2 = 24, find k.

  14. If α and β are the zeroes of the polynomial p(x) = 2x2 + 5x + k, satisfying the relation, α2 + β2 + αβ = 21/4 then find the value of k.

  15. Find the condition that zeroes of polynomial p(x) = ax2 + bx + c are reciprocal of each other.

DAY-2

  1. Find a quadratic polynomial, the sum and product of whose zeroes are √3 and 1/√3.

  2. Find a quadratic polynomial, the sum and product of whose zeroes are 0 and -√2 respectively.

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

  4. Find a quadratic polynomial whose zeroes are (3+√55)/5 and (3−√55)/5 .

  5. Verify whether 2, 3 and 1/2 are the zeroes of the polynomial p(x) = 2x3 – 11x2 + 17x – 6.

  6. Find a quadratic polynomial, the sum and product of whose zeroes are -8 and 12 respectively. Hence find the zeroes.

  7. Find a quadratic polynomial, the sum and product of whose zeroes are 0 and −3/5 respectively. Hence find the zeroes.

  8. If α and β are the zeroes of the polynomial 6y2 – 7y + 2, find a quadratic polynomial whose zeroes are 1/α and 1/β.

  9. Given that x – √5 is a factor of the polynomial x3 – 3√5 x2 – 5x + 15√5, find all the zeroes of the polynomial.

  10. What must be subtracted from the polynomial f(x) = x4 + 2x3 – 13x2 – 12x + 21 so that the resulting polynomial is exactly divisible by x2 – 4x + 3?

  11. Divide 3x2 + 5x – 1 by x + 2 and verify the division algorithm.

  12. On dividing 3x3 + 4x2 + 5x – 13 by a polynomial g(x) the quotient and remainder were 3x +10 and 16x – 43 respectively. Find the polynomial g(x).

  13. Check whether polynomial x – 1 is a factor of the polynomial x3 – 8x2 + 19x – 12. Verify by division algorithm.

  14. Divide 4x3 + 2x2 + 5x – 6 by 2x2 + 1 + 3x and verify the division algorithm.

  15. Given that x – √5 is a factor of the polynomial x3 – 3√5 x2 – 5x + 15√5, find all the zeroes of the polynomial.

DAY-3

  1. If a polynomial x4 + 5x3 + 4x2 – 10x – 12 has two zeroes as -2 and -3, then find the other zeroes.

  2. Find all the zeroes of the polynomial 8x4 + 8x3 – 18x2 – 20x – 5, if it is given that two of its zeroes are √5/2 and -√5/2.

  3. What must be subtracted from p(x) = 8x4 + 14x3 – 2x2 + 8x – 12 so that 4x2 + 3x – 2 is factor of p(x)? This question was given to group of students for working together.

  4. What must be subtracted from p(x) = 8x4 + 14x3 – 2x2 + 8x – 12 so that 4x2 + 3x – 2 is factor of p(x)? This question was given to group of students for working together.

  5. If a polynomial 3x4 – 4x3 – 16x2 + 15x + 14 is divided by another polynomial x2 – 4, the remainder comes out to be px + q. Find the value of p and q.

  6. If the polynomial (x4 + 2x3 + 8x2 + 12x + 18) is divided by another polynomial (x2 + 5), the remainder comes out to be (px + q), find the values of p and q.

  7. Can (x – 2) be the remainder on division of a polynomial p(x) by (2x + 3)? Justify your answer.

  8. 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:(NCERT 2.4)

    (i) 2x3 + x2 – 5x + 2;  1/4, 1, -2

    (ii) x3 – 4x2 + 5x – 2; 2, 1, 1

  9. Find a cubic polynomial with the sum, some of the product of its zeroes taken two at a time, and the product of its zeroes as 2, -7, -14 respectively.(NCERT 2.4)

  10. If the zeroes of the polynomial x3 – 3x2 + x + 1 are a-b, a, a + b, find a and b.(NCERT 2.4)

  11. If two zeroes of the polynomial x4 – 6x3 – 26x2 + 138x – 35 are 2 ± √3, find other zeroes.(NCERT 2.4)

  12. 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 2.4)

  13. REVISE NCERT ALL QUESTONS.

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