Question

Find the zeroes of the polynomial $p\left(x\right)=x^2-4x+3$ and verify the relationship between zeroes and coefficients

Answer 1

Given, $p\left(x\right)=x^2-4x+3$

$=x^2-3x-x+3$

$=x(x-3)-1(x-3)$

$=(x-3)(x-1)$

For zeroes of polynomial, $p\left(x\right)=0$

i.e. $(x-3)(x-1)=0$

or, $x=3$ or $x=1$

Let, $\alpha =3$ and $\beta =1$

$\alpha +\beta =\frac{-b}{a}$

$\alpha \beta =\frac{c}{a}$

Here, $a=1b=-4c=3$

$\alpha +\beta =4$

$\alpha \beta =3$