Notes: Find the roots of the equation using the method of factoring. x^2 - 10x + 25 = 0Show the complete solution and explain the answer.

Thursday, November 12, 2015

You could also apply quadratic formula to determine the
factors of the given quadratic.

Let's recall the formula
first:

$\displaystyle{x}_{{{1},{2}}}={\left[-{b}\pm\sqrt{{{{b}}^{{2}}-{4}{a}{c}}}\right.}$
)]/(2a)

We'll identify the coefficients
a,b,c:

a = 1 ; b = -10 and c =
25

$\displaystyle{x}_{{{1},{2}}}={\left({10}\pm\sqrt{{{100}-}}\right.}$
100))/2

$\displaystyle{x}_{{{1},{2}}}=\frac{{10}}{{2}}$

$\displaystyle{x}_{{1}}$
= x_2 = 5

We notice that the roots of equation are equal,
therefore we can re-write the quadratic:

$\displaystyle{\left({x}-{x}_{{1}}\right)}{\left({x}-\right.}$
x_2) = 0

$\displaystyle{\left({x}-{5}\right)}{\left({x}-{5}\right)}=$
0

$\displaystyle{{\left({x}-{5}\right)}}^{{2}}=$
0

Therefore, the quadratic equation will
have two equal solutions $\displaystyle{x}_{{1}}={x}_{{2}}={5}.$

Notes