Question

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

(a) 1 (b) 2 (c) (d) infinitely many


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Answer 1

Answer:

A

1

B

2

C

3

D

more than 3

Answer

D

Solution

Let p(x)=ax2+bx+c be the required polynomial whose zeroes are -2 and 5.

∴ Sum of zeroes =−ba

⇒−ba=−2+5=31=−(3)1

and product of zeroes =ca

⇒ca=−2×5=−101

From Eqs. (i) and (ii),

a=1,b=−3 and c=−10

∴p(x)=ax2+bx+c=1x2−3x−10

=x2−3x−10

But we know that, if we multiply/divide any polynomial by any arbitary constant. Then, the zeroes of polynomial never change.

∴p(x)=kx2−3kx−10k [where, k is a real number]

⇒p(x)=x2k−3kx−10k, [where,k is a non-zero real number]

Hence, the required number of polynomials are infinite i.e., more than 3.