Question

Find the zeros of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients:

$x^2-4x-5$

• A. 2 or -1
• B. -5 or 0
• C. 5 or -1
• D. 2 or 1

Answer 1

The correct option is C 5 or -1

Let $f\left(x\right)=x^2-4x-5$

The zero of the polynomial is given by $f\left(x\right)=0$

$=>x^2-4x-5=0$
$=>x^2-5x+x-5=0$
$=>x(x-5)+1(x-5)=0$
$=>(x-5)(x+1)=0$

Thus,
$x-5=0$ and $x+1=0$
$=>x=5$ and $=>x=-1$

Thus, zeros of the polynomial are $5$,$-1$

Comparing $f\left(x\right)$ with standard form of quadratic polynomial $a{x}^2+bx+c$

Here, $a=1$, $b=-4$, $c=5$

Sum of the zeros $=5+(-1)$
$=4$
$=\frac{-b}{a}$
$=\frac{-(-4)}{1}$

Product of the zeros$=\left(5\right)(-1)$
$=-5$
$=\frac{c}{a}$
$=\frac{-5}{1}$