## Sunday, July 1, 2012

### Polynomial - Practice Questions

1. The graph of y = p(x) are drawn below. Find the number of zeros in each case:
2. 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) = x3+x-1 c) p(x) = (2/3)x3+1 d) t(x) = x2+5x+1
3. If α, β are zeroes of the polynomial p(x) = 2x2- 4x+5 , find the value of a) α 22 b) (α- β)2
4. If the sum of zeroes of the polynomial p(x) =2x3-3ax2+4x-5 is 6 , then find the value of a.
5. If the product of two zeroes of the polynomial p(x) = 2x3+6x2-4x+9 is 3, then find its third zero.
6. If one zero of the polynomial p(x) = 5x2+13x-a is reciprocal of the other, find the value of a.
7. If α, β are zeroes of the polynomial p(x) x2-(k+6)x+2(2k-1) , find k if 2(α+ β) =α β
8. 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) = 2x2 – 9 – 3x b) q(s) = 2s2+5x+3 c) p(t)=t2-5 d) p(u)=4u2+8u
9. Show that –1 , 3 and 6 are the zeroes of the polynomial p(x) =x3-8x2+9x+18. Also verify the relationship between the zeroes and the coefficients of p(x).
10. 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
11. On dividing 3x3-2x2+5x-5 by a polynomial p(x) , the quotient and remainder are x2-x+2 and –7 respectively. Find p(x).
12. By division algorithm, check whether or not x2+3x+1 is a factor of 3x4+5x3-7x2+2x+2
13. Find the value of b for which the polynomial 2x+3 is a factor of 2x3+9x2-x-b.
14. What must be suptracted from 4x4+2x3-8x2+3x-7 so that it may be exactly divisible by 2x2+x-2?
15. If α , β , γ are the zeros the polynomial 6x3+3x2-5x+1 , then find the value of α-1-1-1
16. If the polynomial 6x4+8x3+17x2+21x+7 is divided by another polynomial 3x2+4x+1 , the remainder comes out to be (ax+b) , find a and b.
17. Find all the zeroes of the polynomial 2x4+7x3-19x2-14x+30 , if two of its zeroes are √2 and -√2
18. If one zero of the polynomial (a2+9)x2+13x+6a is reciprocal of the other. Find the value of a.
19. Find the zeroes of a polynomial f(x) = x3-5x2-16x+80 , if its two zeroes are equal in magnitude but opposite in sign.
20. 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.

#### 1 comment:

1. 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.