10th Class Mathematics Polynomials Question Bank MCQs - Polynomials

If \[a+b+c=0,\] then a zero of the polynomial \[a{{x}^{2}}+bx+c,\]is:

A) \[1\]

B) \[0\]

C) \[-1\]

D) \[\frac{1}{2}\]

Correct Answer: A

Solution :

[a] Given, \[a+b+c=0\]

Let \[f(x)=a{{x}^{2}}+bx+c\]

If \[x=1\] is a zero of \[f(x),\]

Then \[f(1)=0\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,a{{(1)}^{2}}+b(1)+c=0\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,a+b+c=0\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0=0\] (which is true)