# DPP Class 10 Polynomials

## DAY – 1

#### Find the zeroes of the quadratic polynomial 6x

^{2}– 3 – 7x and verify the relationship between the zeroes and the coefficients of the polynomial.#### Find the zeroes of p(x) = 2x

^{2}– x – 6 and verify the relationship of zeroes with these co-efficients.#### Find the zeroes of the quadratic polynomial f(x) = x

^{2}– 3x – 28 and verify the relationship between the zeroes and the co-efficients of the polynomial#### Find the zeroes of the quadratic polynomial 3x

^{2}– 75 and verify the relationship between the zeroes and the coefficients.#### Find the quadratic polynomial whose zeroes are -2 and -5. Verify the relationship between zeroes and coefficients of the polynomial.

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

#### If the sum of the zeroes of the polynomial p(x) = (k

^{2}– 14) x^{2}– 2x – 12 is 1, then find the value of k.#### If the sum of zeroes of the quadratic polynomial 3x

^{2}– kx + 6 is 3, then find the value of k.#### If α and β are the zeroes of a polynomial such that α + β = -6 and αβ = 5, then find the polynomial.

#### If α and β are the zeroes of the polynomial ax

^{2}+ bx + c, find the value of α^{2}+ β^{2}.#### If the zeroes of the polynomial x

^{2}+ px + q are double in value to the zeroes of 2x^{2}– 5x – 3, find the value of p and q.#### Form a quadratic polynomial whose zeroes are 3 + √2 and 3 – √2.

#### If α and β are zeroes of p(x) = kx

^{2}+ 4x + 4, such that α^{2}+ β^{2}= 24, find k.#### If α and β are the zeroes of the polynomial p(x) = 2x

^{2}+ 5x + k, satisfying the relation, α^{2}+ β^{2}+ αβ = 21/4 then find the value of k.#### Find the condition that zeroes of polynomial p(x) = ax

^{2}+ bx + c are reciprocal of each other.

## DAY-2

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

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

#### Find the zeroes of the quadratic polynomial √3 x

^{2}– 8x + 4√3.#### Find a quadratic polynomial whose zeroes are (3+√55)/5 and (3−√55)/5 .

#### Verify whether 2, 3 and 1/2 are the zeroes of the polynomial p(x) = 2x

^{3}– 11x^{2}+ 17x – 6.#### Find a quadratic polynomial, the sum and product of whose zeroes are -8 and 12 respectively. Hence find the zeroes.

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

#### If α and β are the zeroes of the polynomial 6y

^{2}– 7y + 2, find a quadratic polynomial whose zeroes are 1/α and 1/β.#### Given that x – √5 is a factor of the polynomial x

^{3}– 3√5 x^{2}– 5x + 15√5, find all the zeroes of the polynomial.#### What must be subtracted from the polynomial f(x) = x

^{4}+ 2x^{3}– 13x^{2}– 12x + 21 so that the resulting polynomial is exactly divisible by x^{2}– 4x + 3?#### Divide 3x

^{2}+ 5x – 1 by x + 2 and verify the division algorithm.#### On dividing 3x

^{3}+ 4x^{2}+ 5x – 13 by a polynomial g(x) the quotient and remainder were 3x +10 and 16x – 43 respectively. Find the polynomial g(x).#### Check whether polynomial x – 1 is a factor of the polynomial x

^{3}– 8x^{2}+ 19x – 12. Verify by division algorithm.#### Divide 4x

^{3}+ 2x^{2}+ 5x – 6 by 2x^{2}+ 1 + 3x and verify the division algorithm.#### Given that x – √5 is a factor of the polynomial x

^{3}– 3√5 x^{2}– 5x + 15√5, find all the zeroes of the polynomial.

## DAY-3

#### If a polynomial x

^{4}+ 5x^{3}+ 4x^{2}– 10x – 12 has two zeroes as -2 and -3, then find the other zeroes.#### Find all the zeroes of the polynomial 8x

^{4}+ 8x^{3}– 18x^{2}– 20x – 5, if it is given that two of its zeroes are √5/2 and –√5/2.#### What must be subtracted from p(x) = 8x

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

^{4}+ 14x^{3}– 2x^{2}+ 8x – 12 so that 4x^{2}+ 3x – 2 is factor of p(x)? This question was given to group of students for working together.#### If a polynomial 3x

^{4}– 4x^{3}– 16x^{2}+ 15x + 14 is divided by another polynomial x^{2}– 4, the remainder comes out to be px + q. Find the value of p and q.#### 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 values of p and q.#### Can (x – 2) be the remainder on division of a polynomial p(x) by (2x + 3)? Justify your answer.

#### 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) 2x

^{3}+ x^{2}– 5x + 2; 1/4, 1, -2#### (ii) x

^{3}– 4x^{2}+ 5x – 2; 2, 1, 1#### 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)

#### If the zeroes of the polynomial x

^{3}– 3x^{2}+ x + 1 are a-b, a, a + b, find a and b.(NCERT 2.4)#### If two zeroes of the polynomial x

^{4}– 6x^{3}– 26x^{2 }+ 138x – 35 are 2 ± √3, find other zeroes.(NCERT 2.4)#### If the polynomial x

^{4}– 6x^{3}+ 16x^{2}– 25x + 10 is divided by another polynomial x^{2}– 2x + k, the remainder comes out to be x + a, find k and a.(NCERT 2.4)#### REVISE NCERT ALL QUESTONS.

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