Question

Are the zeroes of the quadratic polynomial x2 + 50x + 141 negative or positive? And why?

Answer 1

Sum of zeroes = -50

Product = 141

Since the sum of negative and product is positive, this is possible only when the numbers/zeroes are both negative

As, the product of two negative numbers is always positive and their sum is always negative.

Hope it helps you! :)

Answer 2

$\red{\tt{\underline{\underline{Answer:}}}}$

$\sf{Zeroes \ are \ negative.}$

$\orange{\tt{\underline{\underline{Given:}}}}$

$\sf{The \ given \ quadratic \ polynomial \ is}$

$\sf{\implies{x^{2}+50x+141}}$

$\pink{\tt{\underline{\underline{To \ find:}}}}$

$\sf{Nature \ of \ zeroes.}$

$\green{\tt{\underline{\underline{Solution:}}}}$

$\sf{The \ given \ quadratic \ polynomial \ is}$

$\sf{\implies{x^{2}+50x+141}}$

$\sf{Here, \ a=1, \ b=50 \ and \ c=141}$

$\sf{Sum \ of \ zeroes=\frac{-b}{a}}$

$\sf{\therefore{Sum \ of \ zeroes=-50}}$

$\sf{Product \ of \ zeroes=\frac{c}{a}}$

$\sf{\therefore{Product \ of \ zeroes=141}}$

$\sf{But, \ it \ is \ only \ possible \ when,}$

$\sf{both \ zeroes \ are \ negative.}$

______________________________

$\bold\blue{\underline{\underline{Verification}}}$

$\sf{The \ given \ quadratic \ polynomial \ is}$

$\sf{\implies{x^{2}+50x+141}}$

$\sf{\implies{x^{2}+3x+47x+141}}$

$\sf{\implies{x(x+3)+47(x+3)}}$

$\sf{\implies{(x+3)(x+47)}}$

$\sf{\therefore{\implies{x= -3 \ or \ -47}}}$

$\sf{\therefore{Zeroes \ are \ negative.}}$