10th Class Mathematics Polynomials Question Bank Case Based (MCQs) - Polynomials

The zeroes of the quadratic polynomial \[{{x}^{2}}+20x+96\]are:

A) both positive

B) both negative

C) one positive and other negative

D) both equal

Correct Answer: B

Solution :

Let \[f(x)={{x}^{2}}+20x+96\]

[\[96=12\times 8=6\times 16=2\times 48.....\]

\[\therefore \]Here, we will take 12 and 8 as a factors of 96.

So, middle term is \[20=12+8\]]

\[={{x}^{2}}+12x+8x+96\]

\[=x(x+12)+8(x+12)\]

\[=(x+12)\,\,(x+8)\]

For the zeroes of \[f(x),\]

\[x+12=0\] or \[x+8=0\]

\[\therefore \,\,\,\,x=-8,-12\]

i.e., both zeroes are negative

So, option [b] is correct.