Question

The number of polynomial having zeroes as -2 and 5 is
a)1
b)2
c)3
d)more than 3

Answer 1

Step-by-step explanation:

Correct option is D more than 3

Polynomial having zero as 2 and 5 is of the form:

P(x)=a(x−2) n(x−5) m

,

where n and m can take any value from 1,2,3,

Therefore, there can be infinite polynomials having zero as 2 and 5.

Hence, the number of polynomials is >3.

Answer 2

The number of polynomial having zeroes as - 2 and 5 is more than 3

Given :

The zeroes of the polynomial as - 2 and 5

To find :

The number of polynomial having zeroes as - 2 and 5 is

a) 1

b) 2

c) 3

d) more than 3

Solution :

Step 1 of 2 :

Write down the zeroes of the polynomial

The zeroes of the polynomial are - 2 and 5

Step 2 of 2 :

Find the number of polynomial

Let - 2 & 5 are zeroes of the polynomial of multiplicity m and n respectively

Where m and n are natural numbers

Then the polynomial is of the form

$\sf = a {(x + 2)}^{m} {(x - 5)}^{n}$

Where a is the leading coefficient

So number of such polynomial is infinite

Thus the number of polynomial having zeroes as - 2 and 5 is more than 3

Hence the correct option is d) more than 3

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