10th Class Mathematics Polynomials Question Bank MCQs - Polynomials

If two of the zeroes of the cubic polynomial \[a{{x}^{3}}+b{{x}^{2}}+cx+d\] are each equal to zero, then the third zero is:

A) \[-\frac{d}{a}\]

B) \[\frac{c}{a}\]

C) \[-\frac{b}{a}\]

D) \[\frac{b}{a}\]

Correct Answer: C

Solution :

[c] The given polynomial is \[a{{x}^{3}}+b{{x}^{2}}+cx+d.\]

Now, two of the zeroes of given polynomial are equal to zero.

[Given]

Let the third zero be \[\alpha \].

\[\therefore \] Sum of zeroes \[=0+\alpha =-\frac{b}{a}\Rightarrow \alpha =-\frac{b}{a}\]