Question

If two zeroes of the polynomial representing the given curve are 5 and -2 then the

polynomial is:​

Answer 1

Answer:

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.