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Formula notes and concepts 

EXERCISE 2.1

1 
The graphs of y = p(x) are given in Fig. 2.10 below, for some polynomials p(x). Find the number of zeroes of p(x), in each case. (all solutions) 

EXERCISE 2.2 
1 
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. (i) x2 – 2x – 8 (ii) 4s2 – 4s + 1 (iii) 6x2 – 3 – 7x (iv) 4u2 + 8u (v) t2 – 15 (vi) 3x2 – x – 4 
2 
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. (i)1/4 , 1 (ii) √2 , 1/3 (iii) 0, √5 (iv) 1,1 (v) 1/4 ,1/4 (vi) 4,1 

EXERCISE 2.3 
1 
Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following : (i) p(x) = x3 – 3x2 + 5x – 3, g(x) = x2 – 2 (ii) p(x) = x4 – 3x2 + 4x + 5, g(x) = x2 + 1 – x (iii) p(x) = x4 – 5x + 6, g(x) = 2 – x2

2 
Check whether the first polynomial is a factor of the second polynomial by dividing the
second polynomial by the first polynomial:
(i) t2 – 3, 2t4 + 3t3 – 2t2 – 9t – 12
(ii) x2 + 3x + 1, 3x4 + 5x3 – 7x2 + 2x + 2
(iii) x3 – 3x + 1, x5 – 4x3 + x2 + 3x + 1 
3 
Obtain all other zeroes of 3x4 + 6x3 – 2x2 – 10x – 5, if two of its zeroes are √(5/3) and  √(5/3) 
4 
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). 
5 
Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm
and
(i) deg p(x) = deg q(x) (ii) deg q(x) = deg r(x) (iii) deg r(x) = 0 
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