10th Class Mathematics Polynomials Question Bank MCQs - Polynomials

If \[\alpha ,\beta \] are the zeroes of the polynomial \[{{x}^{2}}+5x+c,\] and \[\alpha -\beta =3,\] then c =

A) 0

B) 1

C) 4

D) 5

Correct Answer: C

Solution :

[c] Since \[\alpha ,\beta \] are zeroes of the polynomial \[{{x}^{2}}+5x+c\]

\[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\alpha +\beta =-5\] ...(1)

and \[\alpha -\beta =3\] (Given) ,..(2)

On solving eqs. (1) and (2), we have\[\alpha =-1\] and \[\beta =-4\]

Now, product of zeroes \[=\alpha \beta =(-1)\,(-4)=4\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,c=4\]