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Class 10 Maths Problems for Polynomial



1) Verify that 3, -1, -1/3  are the zeroes of the cubic polynomial coefficients.
2) Verify that -5,1/2,3/4  are zeroes of cubic polynomial 4y3 + 20y + 2y -3. Also verify the relationship between the zeroes and the coefficients.
3) Using division show that 3x2 + 5 is a factor of 6x5 + 15x4 + 16x3 + 4x2 + 10x – 35.
4) Using division state whether 2y – 5 is a factor of 4y4 – 10y3 – 10y2 + 30y – 15.
5) Check whether g(x) = x2 – 3 is a factor of p(x) = 2x4 + 3x3 – 2x2 – 9x – 12 by applying division algorithm.
6) Check whether p(x) = x2 +3x +1 is a factor of g(x) = 3x4 + 5x2 – 7x2 + 2x + 2 by using division algorithm.
7) Find remainder when x3 – bx2 + 5 – 2b is divided by x – b.
8) Check whether polynomial x – 3 is a factor of the polynomial x3 – 3x2 – x + 3. Verify by division algorithm.
9) If 4x4 + 7x3 – 4x2 – 7x + p is completely divisible by x3 – x, then find the value of p.
10) If α and β are the zeroes of the quadratic polynomial f(x) = kx2 + 4x + 4 such that α2 + β2 = 24, find the values of k.
11) If α and β are the zeroes of the quadratic polynomial f(x) = 2x2 – 5x + 7, find a polynomial whose zeroes are 2α + 3β and 3α + 2β.
12) If the squared difference of the zeroes of the quadratic polynomial
f(x) = x2 + px + 45 is equal to 144, find the value of p.
13) If α and β are the zeroes of the quadratic polynomial f(x) = x2 – p (x + 1) – c, show that (α + 1) (β + 1) = 1 – c.
14) 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?
15) Verify that 1, 2 and -1/2 are zeroes of 2x3 – 5x2 + x + 2. Also verify the relationship between the zeroes and the coefficients.
16) On dividing the polynomial 4x4 – 5x3 – 39x2 – 2 by the polynomial g(x), the quotient is x2 – 3x -5 and the remainder is -5x + 8. Find the polynomial g(x).
17) If α and β are the zeroes of the polynomial f(x) = x2 + px + q, form a polynomial whose zeroes are (α + β)2 and (α – β)2.
18) On dividing the polynomial 4x4 – 5x3 – 39x2 – 2 by the polynomial g(x), the quotient and remainder were x2 – 3x – 5 and -5x + 8 respectively. Find g(x).

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