# Polynomials

1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.
(i) 4u2 + 8u
(ii) t2 – 15
(iii) 3x2 – x – 4
(iv) 4s2 – 4s + 1

2. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
(i) 1/4, -1
(ii) 0, √5
(iii) √2, 1/3

3. Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following.

(i) p(x) = x4 – 3x2 + 4x + 5, g(x) = x2 + 1 – x
(ii) p(x) = x4 – 5x + 6, g(x) = 2 – x2

4. Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial.
(i) x3 – 3x + 1, x5 – 4x3 + x2 + 3x + 1
(ii) x2 + 3x + 1, 3x4 + 5x3 – 7x2 + 2x + 2

5. Obtain all other zeroes of 3x4 + 6x3 – 2x2 – 10x – 5, if two of its zeroes are √(5/3) and –√(5/3)

6. On dividing (x3 – 3x2 + x + 2) by a polynomial g(x), the quotient and remainder were (x – 2) and (–2x + 4), respectively. Find g(x).

7. If one zero of the quadratic polynomial x2 + 3x + k is 2, then calculate the value of k.

8. Find the zeroes of the following polynomials by factorization method and verify the relations between the zeroes and the coefficients of the polynomials:

(i) 4x2 – 3x – 1
(ii) 3x2 + 4x – 4

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