10th Class Mathematics Polynomials Question Bank MCQs - Polynomials

The zeroes of the quadratic polynomial \[{{x}^{2}}+kx+k,\]where \[\text{k}>0\]:

A) are both positive

B) are both negative

C) are always equal

D) are always unequal

Correct Answer: B

Solution :

[b] Let \[\alpha \] and \[\beta \] be the zeroes of\[{{x}^{2}}+kx+k.\]

Then, \[\alpha +\beta =-k\] and \[\alpha \beta =k\]

This is possible only when \[\alpha \] and \[\beta \] are both negative.