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The number of polynomials having zeroes as –2 and 5 is
CBSE | Class 10 | Exercise 2.1 | Maths | NCERT Exemplar | Polynomials
The number of polynomials having zeroes as –2 and 5 is

(A) 1 (B) 2 (C) 3 (D) more than 3

(D) more than 3

Clarification:

As per the inquiry,

The zeroes of the polynomials = – 2 and 5

We realize that the polynomial is of the structure,

    \[p\left( x \right)\text{ }=\text{ }ax2\text{ }+\text{ }bx\text{ }+\text{ }c.\]

Amount of the zeroes = – (coefficient of x) ÷ coefficient of x2 for example

Amount of the zeroes = – b/a

    \[\text{ }2\text{ }+\text{ }5\text{ }=\text{ }\text{ }b/a\]

3 = – b/a

b = – 3 and a = 1

Result of the zeroes = consistent term ÷ coefficient of x2 for example

Result of zeroes = c/a

    \[\left( -\text{ }2 \right)5\text{ }=\text{ }c/a\]

– 10 = c

Subbing the upsides of a, b and c in the polynomial

    \[p\left( x \right)\text{ }=\text{ }ax2\text{ }+\text{ }bx\text{ }+\text{ }c.\]

We get,

    \[x2\text{ }\text{ }3x\text{ }\text{ }10\]

Consequently, we can reason that x can take any worth.

Thus, alternative (D) is the right reply.

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