DPP Class 10 Polynomials
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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 coefficients.

Find the zeroes of the quadratic polynomial f(x) = x^{2} – 3x – 28 and verify the relationship between the zeroes and the coefficients 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.
DAY2

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.
DAY3

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 ab, 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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