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Solution not provided. Ans. Quotient = 3x 3 + x 2 – 2x – 5, remainder = 3,

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Polynomials

Short Answer Type

491. Apply the division algorithm to find the quotient and the remainder in division of p(x) by g(x) as given below:
p(x) = 24x² – 65x + 22, g(x) = 8x – 3.

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492. Apply the division algorithm to find the quotient and the remainder in division of p(x) by g(x) as given below:
p(x) = 6x⁵ – x⁴ + 4x³ – 5x² – x – 12, g(x) = 2x² + 3 – x.

Solution not provided.
Ans. Quotient = 3x³ + x²– 2x – 5, remainder = 3,

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493. Apply the division algorithm to find the quotient and the remainder in division of p(x) by g(x) as given below:
p(x) = 4 + x⁴; g(x) = 2x + 2 + x².

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494. Apply the division algorithm to find the quotient and the remainder in division of p(x) by g(x) as given below:
p(x) = 3x + 1 + 2x²; g(x) = x + 2.

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495. Apply the division algorithm to find the quotient and the remainder in division of p(x) by g(x) as given below:
p(x) = 5 + x² + 3x³ + 2x; g(x) = 2x + 1 + x².

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Long Answer Type

496. Check whether the first polynomial is a factor of the second polynomial by the division algorithm:
(i) g(t) = t² –3, f(t) = 2t⁴ + 3t³ – 2t² – 9t – 12
(ii) g(x)= x³ –3x + 1, f(x) = x⁵ – 4x³ + x² + 3x + 1

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497. Obtain all zeroes of the polynomial f(x) = 2x⁴ + x³ – 14x² – 19x – 6, if two of its zeroes are -2 and -1.

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498. Find all zeroes of the polynomial f(x) = 2x⁴ – 2x³ – 7x² + 3x + 6, if its two zeroes are

negative square root of 3 over 2 end root space and space square root of 3 over 2 end root.

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Short Answer Type

499. If α and β are the zeroes of the quadratic polynomial p(x) = 2x² – 5x + 7, Find a polynomial whose zeroes are (2α + 3β) and (3α + 2β).

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500. If α and β are the zeroes of the quadratic polynomial f(x) = x² – 4x + 3, find the value of α⁴β³ + α³β⁴.

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Previous Year Papers

Test Series

Test Yourself

Short Answer Type

492. Apply the division algorithm to find the quotient and the remainder in division of p(x) by g(x) as given below:p(x) = 6x5 – x4 + 4x3 – 5x2 – x – 12, g(x) = 2x2 + 3 – x.

Long Answer Type

Short Answer Type

492. Apply the division algorithm to find the quotient and the remainder in division of p(x) by g(x) as given below:
p(x) = 6x⁵ – x⁴ + 4x³ – 5x² – x – 12, g(x) = 2x² + 3 – x.