Question

Completing the square to find the zeros3. a^2+2a-3=0

Answer 1

1 and -3.

Step-by-step explanation:

Given the quadratic polynomial:

`a^2+2a-3=0`

To use the completing the square method to find the zeros, follow the steps below:

Step 1: Take the constant to the right-hand side.

`a^2+2a=3`

Step 2: Divide the coefficient of a by 2, square it and add it to both sides.

`a^2+2a+(1)^2=3+(1)^2`

Step 3: Write the left-hand side as a perfect square.

`(a+1)^2=4`

Step 4: Take the square root of both sides.

`a+1=\pm\sqrt[]{4}`

Step 5: Solve for a.

`\begin{gathered} a=-1\pm\sqrt[]{4} \\ a=-1\pm2 \\ a=-1+2\text{ or }a=-1-2 \\ a=1\text{ or }a=-3 \end{gathered}`

The zeros of the quadratic equation are 1 and -3.