DPP Class 10 Polynomials
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DAY – 1
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Find the zeroes of the quadratic polynomial 6x2 – 3 – 7x and verify the relationship between the zeroes and the coefficients of the polynomial.
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Find the zeroes of p(x) = 2x2 – x – 6 and verify the relationship of zeroes with these co-efficients.
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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
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Find the zeroes of the quadratic polynomial 3x2 – 75 and verify the relationship between the zeroes and the coefficients.
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Find the quadratic polynomial whose zeroes are -2 and -5. Verify the relationship between zeroes and coefficients of the polynomial.
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Write the quadratic polynomial, whose zeroes are -4 and -5
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If the sum of the zeroes of the polynomial p(x) = (k2 – 14) x2 – 2x – 12 is 1, then find the value of k.
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If the sum of zeroes of the quadratic polynomial 3x2 – kx + 6 is 3, then find the value of k.
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If α and β are the zeroes of a polynomial such that α + β = -6 and αβ = 5, then find the polynomial.
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If α and β are the zeroes of the polynomial ax2 + bx + c, find the value of α2 + β2.
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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.
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Form a quadratic polynomial whose zeroes are 3 + √2 and 3 – √2.
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If α and β are zeroes of p(x) = kx2 + 4x + 4, such that α2 + β2 = 24, find k.
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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.
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Find the condition that zeroes of polynomial p(x) = ax2 + bx + c are reciprocal of each other.
DAY-2
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Find a quadratic polynomial, the sum and product of whose zeroes are √3 and 1/√3.
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Find a quadratic polynomial, the sum and product of whose zeroes are 0 and -√2 respectively.
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Find the zeroes of the quadratic polynomial √3 x2 – 8x + 4√3.
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Find a quadratic polynomial whose zeroes are (3+√55)/5 and (3−√55)/5 .
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Verify whether 2, 3 and 1/2 are the zeroes of the polynomial p(x) = 2x3 – 11x2 + 17x – 6.
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Find a quadratic polynomial, the sum and product of whose zeroes are -8 and 12 respectively. Hence find the zeroes.
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Find a quadratic polynomial, the sum and product of whose zeroes are 0 and −3/5 respectively. Hence find the zeroes.
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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.
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Given that x – √5 is a factor of the polynomial x3 – 3√5 x2 – 5x + 15√5, find all the zeroes of the polynomial.
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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?
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Divide 3x2 + 5x – 1 by x + 2 and verify the division algorithm.
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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).
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Check whether polynomial x – 1 is a factor of the polynomial x3 – 8x2 + 19x – 12. Verify by division algorithm.
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Divide 4x3 + 2x2 + 5x – 6 by 2x2 + 1 + 3x and verify the division algorithm.
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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
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If a polynomial x4 + 5x3 + 4x2 – 10x – 12 has two zeroes as -2 and -3, then find the other zeroes.
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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.
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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.
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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.
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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.
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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.
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Can (x – 2) be the remainder on division of a polynomial p(x) by (2x + 3)? Justify your answer.
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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
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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)
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If the zeroes of the polynomial x3 – 3x2 + x + 1 are a-b, a, a + b, find a and b.(NCERT 2.4)
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If two zeroes of the polynomial x4 – 6x3 – 26x2 + 138x – 35 are 2 ± √3, find other zeroes.(NCERT 2.4)
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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)
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REVISE NCERT ALL QUESTONS.
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