Question

and write your 1. Give at least one example of quadratic equation that can be solved by extracting square roots with a. two real solutions b. one real solution c. no real solution. trenresents the area of each square. ​

Answer 1

Answer:The equation 4x2−9=0 is in this form and can be solved by first isolating x2. Applying the square root property as a means of solving a quadratic equation is called extracting the root3. This method allows us to solve equations that do not factor.

Step-by-step explanation:

Answer 2

Tip:

• By applying the square root property as a means of solving a quadratic equation is called extracting the square root.
• This method allows us to solve equations that do not get factorize.

Step

Step 1 of 2:

a.) Having two real solutions

Let the quadratic equation be $9x^2-8=0$

Notice that the quadratic expression on the left does not factor. However, it is in the form of $ax^2+c=0$ and we can solve it by extracting the roots:

$9x^2-8=0\\9x^2=8\\x^2=\frac{8}{9}\\x=\pm\sqrt{\frac{8}{9}}\\x=\pm\frac{2\sqrt{2}}{3}$

Two real solutions are $-\frac{2\sqrt{2}}{3},~\frac{2\sqrt{2}}{3}$  

Step 2 of 2:

c.) Having no real solution

Let the quadratic equation be $x^2+25=0$

Notice that the quadratic expression on the left does not factor. However, it is in the form of $ax^2+c=0$ and we can solve it by extracting the roots:

$x^2+25=0\\x^2=-25\\x=\pm\sqrt{-25}\\x=\pm\sqrt{-1\cdot25}\\x=\pm5\iota$

Two complex solutions, $\pm5\iota$ .