Chapter 9.5, Problem 25PPS

To determine

Find the solution.

Answer to Problem 25PPS

No real roots

Explanation of Solution

Given Information: $2x^2-2x+7=5$

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

Calculation:

  $2x^2-2x+7=5$

So, simplify

  $2x^2-2x+7-5=0$

Now,

  $2x^2-2x+2=0$

Now, to make coefficient of $x^2$ = 1, divide the equation by 2.

  $x^2-x+1=0$

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

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

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

Now,

  $D=1-4$

Hence,

  $D=-3$

As, $d$ equal to negative so $x$ has no real roots.