Question

Find the quadratic equation given its roots to be 3^1/2 and plus or minus 2

Answer 1

To find the quadratic equation given its roots, we can use the formula:

\(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)

Given the roots are 3^(1/2) and plus or minus 2, we can write the two equations as:

\(x = 3^{1/2}\)

\(x = 2\)

OR

\(x = -2\)

Using the formula, we have:

For \(x = 3^{1/2}\):

\(3^{1/2} = \frac{-b + \sqrt{b^2 - 4ac}}{2a}\)

Squaring both sides:

\(3 = \frac{b^2 - 4ac}{4a^2}\)

For \(x = 2\):

\(2 = \frac{-b + \sqrt{b^2 - 4ac}}{2a}\)

For \(x = -2\):

\(-2 = \frac{-b - \sqrt{b^2 - 4ac}}{2a}\)

Finally, we can solve these three equations simultaneously to find the values of a, b, and c.