Chapter 9.6, Problem 52HP

To determine

Solve the equation.

Answer to Problem 52HP

  $x=4$

Explanation of Solution

Given Information: $f(x)=x^2-8x+16$

Formula Used:Factorization and $D=b^2-4ac$

Calculation:

  $f(x)=x^2-8x+16$

So,

  $x^2-8x+16=0$

Now, factorise

  $x^2-4x-4x+16=0$

So,

  $x\left(x-4\right)-4\left(x-4\right)=0$

Now,

  $\left(x-4\right)\left(x-4\right)=0$

Now,

  ${\left(x-4\right)}^2=0$

Now, square root both sides

  $\left(x-4\right)=0$

Hence,

  $x=4$

Now, use formula $D=b^2-4ac$ to check if solution of $x$ exist or not.

As $a=1,b=-8$ and $c=16$

  $D={\left(-8\right)}^2-4\times 1\times 16$

Now,

  $D=64-64$

Hence,

  $D=0$

As, $D$ equal to 0 so $x$ has 1 real solution.

Discriminant method is much easier and shorter than factorization method.