Q1. For each of the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials
by factorisation.
- -8/3 , 4/3
- 21/8 , 5/16
- -2√ 3,-9
- -3/2√ 5 , -1/2
Solution:
Q2. Given that the zeroes of the cubic polynomial x3 – 6x2 + 3x + 10 are of the form a, a + b, a + 2b for some real numbers a and b, find the values of a and b as well as the zeroes of the given polynomial.
Solution:
Q3. Given that 2 is a zero of the cubic polynomial 6x3+ 2 x2 – 10x – 4 2 , find its other two zeroes.
Solution:
Q4. Find k so that x2 + 2x + k is a factor of 2x4 + x3 – 14 x2 + 5x + 6. Also find all the zeroes of the two polynomials.
Solution:
Q5. Given that x – 5 is a factor of the cubic polynomial x3
– 3 2 5x + 13x – 3 5 , find all the zeroes of the polynomial.
Solution:
Q6. For which values of a and b, are the zeroes of q(x) = x3 + 2x2
+ a also the zeroes of the polynomial p(x) = x5 – x4– 4x3 + 3x2 + 3x + b? Which zeroes of p(x) are
not the zeroes of q(x)?
Solution:
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