- The graph of y = p(x) are drawn below. Find the number of zeros in each case:
- Check whether the following are polynomials or not. If they are polynomial classify them as linear, quadratic or cubic polynomial. If they are not , give reasons for this.
a) p(x) = √x+3 b) q(x) = x
^{3}+x-1 c) p(x) = (2/3)x^{3}+1 d) t(x) = x^{2}+5x+1 - If α, β are zeroes of the polynomial p(x) = 2x
^{2}- 4x+5 , find the value of a) α^{2}+β^{2}b) (α- β)^{2} - If the sum of zeroes of the polynomial p(x) =2x
^{3}-3ax^{2}+4x-5 is 6 , then find the value of a. - If the product of two zeroes of the polynomial p(x) = 2x
^{3}+6x^{2}-4x+9 is 3, then find its third zero. - If one zero of the polynomial p(x) = 5x
^{2}+13x-a is reciprocal of the other, find the value of a. - If α, β are zeroes of the polynomial p(x) x
^{2}-(k+6)x+2(2k-1) , find k if 2(α+ β) =α β - Find the zeroes of each of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients of the polynomials:
a) p(x) = 2x
^{2}– 9 – 3x b) q(s) = 2s^{2}+5x+3 c) p(t)=t^{2}-5 d) p(u)=4u^{2}+8u - Show that –1 , 3 and 6 are the zeroes of the polynomial p(x) =x
^{3}-8x^{2}+9x+18. Also verify the relationship between the zeroes and the coefficients of p(x). - Find the cubic polynomial with the sum of its zeroes, sum of the products of its zeroes taken two at a time and product of its zeroes being given below: a) 4 , 1 and –6 b) 1 , -1 and 2
- On dividing 3x
^{3}-2x^{2}+5x-5 by a polynomial p(x) , the quotient and remainder are x^{2}-x+2 and –7 respectively. Find p(x). - By division algorithm, check whether or not x2+3x+1 is a factor of 3x
^{4}+5x^{3}-7x^{2}+2x+2 - Find the value of b for which the polynomial 2x+3 is a factor of 2x
^{3}+9x^{2}-x-b. - What must be suptracted from 4x
^{4}+2x^{3}-8x^{2}+3x-7 so that it may be exactly divisible by 2x^{2}+x-2? - If α , β , γ are the zeros the polynomial 6x
^{3}+3x^{2}-5x+1 , then find the value of α^{-1}+β^{-1}+γ^{-1} - If the polynomial 6x
^{4}+8x^{3}+17x^{2}+21x+7 is divided by another polynomial 3x^{2}+4x+1 , the remainder comes out to be (ax+b) , find a and b. - Find all the zeroes of the polynomial 2x
^{4}+7x^{3}-19x^{2}-14x+30 , if two of its zeroes are √2 and -√2 - If one zero of the polynomial (a
^{2}+9)x^{2}+13x+6a is reciprocal of the other. Find the value of a. - Find the zeroes of a polynomial f(x) = x
^{3}-5x^{2}-16x+80 , if its two zeroes are equal in magnitude but opposite in sign. - If α , β are zeroes of a quadratic polynomial such that α + β = 24 and α - β = 8 , find the quadratic polynomial having α , β as its zeroes.

## Sunday, July 1, 2012

### Polynomial - Practice Questions

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In mathematics, a polynomial is an expression of finite length constructed from variables (also called indeterminates) and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents. However the division by a constant is allowed, because the multiplicative inverse of a non zero constant is also a constant.

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