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  • The number of polynomials having zeroes as –2 and 5 is

The number of polynomials having zeroes as –2 and 5 is

(A) 1

(B) 2

(C) 3

(D) more than 3

Answers (1)

Answer.          [D]

Solution. Polynomial : It is an expression of more than two algebraic terms, especially the sum of several terms that contains different powers of the same variable(s).

Let the polynomial is ax^2 + bx + c = 0                  ….(*)

We know that sum of zeroes -\frac{b}{a}      

- 2 + 5= -\frac{b}{a}

         \frac{3}{1}=-\frac{b}{a}       

                                           …..(1)

Multiplication of zeroes =\frac{c}{a}           

-2 \times 5=\frac{c}{a}

-\frac{10}{1}=\frac{c}{a}                 …..(2)

Form equation (1) and (2) it is clear that

a = 1, b = –3, c = –10

put value of a, b and c in equation (*)

x^3 - 3x - 10 = 0                         ….(3)

But we can multiply of divide eqn. (3) by any real number except 0 and the zeroes remain same.

Hence, there are infinite number of polynomial exist with zeroes –2 and 5.

Hence the answer is more than 3.

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