Question

Can anyone teach me plzThis question about mathPlz open to see clearly

Answer 1

Assuming you know the quadratic formula:

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

You can fill in a, b and c in this and get:

$x = \frac{4 \pm \sqrt{16-8p}}{4}$

Now, let's create a shorthand $q = \frac{\sqrt{16-8p}}{4}$ to make the writing easier:

$x = 1 \pm q$

But since one root is three times the other root (but we don't know which one), we also know that:

$1 + q = 3(1-q)$ or $1 - q = 3(1+q)$

If you solve this, you get:

$q = \frac{1}{2}$ or $q = -\frac{1}{2}$

However, since q is a square root, it must be postive.

So we know that:

$\frac{\sqrt{16-8p}}{4} = \frac{1}{2}$

From this you find that

$16-8p = 4$

So p = 3/2

The roots are x=1/2 and x=3/2.