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.
(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:
(ii) 3x2 + 4x – 4
