Chapter 9.7, Problem 36PFA

To determine

Solve the equation.

Answer to Problem 36PFA

Option C

  $k=3$

Explanation of Solution

Given information: $y=x^2-3x+7$ and $y=x+k$

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

Calculation:

For such equations, a graphing utility can often be used to investigate possible solutions. When a graphing utility is used to solve an equation, usually approximate solutions are obtained.

  $y=x^2-3x+7$ and $y=x+k$

Now, equate

  $x^2-3x+7=x+k$

So, simplify

  $x^2-4x+\left(7-k\right)=0$

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

As $a=1,b=-4$ and $c=7-k$

  $D={\left(-4\right)}^2-4\times 1\times \left(7-k\right)$

If, $D$ equal to zero then $x$ has one real solution.

  ${\left(-4\right)}^2-4\times 1\times \left(7-k\right)=0$

So,

  $16-28+4k=0$

Now,

  $4k=12$

So,

  $k=\frac{12}{4}$

Hence,

  $k=3$