Example-2:the number of zeroes of the given polynomials. And also find their values.

1.p(x) = 2x+1     2.q(y) = y²-1     3.r(z) = z³    

Solution We will do this without plotting the graph.

1.p(x) - 2x + 1 is a linear polynomial. It has only one zero.

To find zeroes,

Let p(x) = 0

So, 2x + 1 = 0

Therefore x = - 1/2

The zero of the given polynomial is - 1/2

2. q(y) = y2 - 1 is a quadratic polynomial.

It has at most two zeroes.

To find zeroes, let q(y) = 0

=> y²- 1 = 0

⇒ (y + 1)(y - 1) = 0

=> y = - 1 or y = 1

Therefore the zeroes of the polynomial are-1 and 1.

3. r(z) = z3 is a cubic polynomial. It has at most three zeroes.

Let r(2)-0

=> z³= 0

=> z = 0

So, the zero of the polynomial is 0.




page no:63

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