Question

Find the zeroes of $x^2-25x+84$ and the verify the relationship between zeroes and coefficient.

Answer 1

We have,

$x^2-25x+84$

$=x^2-21x-4x+84$

$=x(x-21)-4(x-21)$

$=(x-21)(x-4)$

So, the value of $x^2-25x+84$ is zero when $x-21=0$ or $x-4=0$

i.e., when $x=21$ or $x=4$

Therefore, the zeroes of $x^2-25x+84$ are $21$ and $4$

Now, Sum of zeroes $=21+4=25=\frac{-(-25)}{1}=\frac{-b}{a}$

Product of zeroes $=21\times 4=84=\frac{84}{1}=\frac{c}{a}$

Hence verified.