Chapter 9.7, Problem 28HP

To determine

Solve the equations.

Answer to Problem 28HP

No Real Solution

Explanation of Solution

Given Information: $y=-2x^2+4x-1$ and $-5x+y=5$

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

Calculation:

  $y=-2x^2+4x-1$ and $-5x+y=5$

So,

  $y=-2x^2+4x-1$ and $y=5+5x$

Now, equate

  $-2x^2+4x-1=5+5x$

So, simplify

  $5+5x+2x^2-4x+1=0$

So,

  $2x^2+x+6=0$

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

As $a=2,b=1$ and $c=6$

  $D={\left(1\right)}^2-4\times 2\times 6$

Now,

  $D=1-48$

Hence,

  $D=-47$

As, $D$ equal to negative so $x$ has no real solution.