We see that p(3) = 0 and p(-1) = 0. 3 and –1 are called Zeroes of the polynomial p(x) = x2– 2x -3

As p(2) not equal to 0, 2 is not zero of p(x)

More generally, a real number k is said to be a zero of a polynomial p(x), if p(k) = 0

Do This

(i) Let p(x) = x2– 4x + 3. Find the value of p(0), p(1), p(2), p(3) and obtain zeroes of the polynomial p(x).

(ii) Check whether -3 and 3 are the zeroes of the polynomial x 2 – 9


EXERCISE - 3.1

 1. In p(x) = 5x7 – 6x5 + 7x-6, what is the

(i) coefficient of x5     (ii) degree of p(x)     (iii) constant term.

2. State which of the following statements are true and which are false? Give reasons for your choice.

(i)The degree of the polynomial √2 x2– 3x + 1 is √2.

(ii)The coefficient of x2in the polynomial p(x) = 3x3– 4x2+ 5x + 7 is 2.

(iii)The degree of a constant term is zero.

(iv)1/x2 - 5x +6is a quadratic polynomial.

(v)The degree of a polynomial is one more than the number of terms in it.

3. If p(t) = t3– 1, find the values of p(1), p(–1), p(0), p(2), p(–2).

4. Check whether –2 and 2 are the zeroes of the polynomial x4– 16.

5. Check whether 3 and –2 are the zeroes of the polynomial p(x) when p(x) = x2 - x - 6



page no:54

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