Question help as maths

It's a quadratic, so rearrange into a more familiar form.
what method do you know to test if an equation has real roots?

no your not.
what was the expression for the discriminant?

Got this in my CCEA AS C1 exam today. Need to know what the answer would be.

(x-p)(x-q)=m^2

Show that the equation has real roots

All you need to do is SHOW that the eq. has real roots, you don't necessarily need to find them here.

$x^2-(p+q)x+pq-m^2 = 0$ from the eq.

Hence for real roots we need that $b^2 - 4ac \geq 0$. Do we have that here??

Clearly, $(p+q)^2 - 4(1)(pq-m^2) = p^2 -2pq + q^2 + m^2 = (p-q)^2 + m^2$

and you are summing two squares, hence obviously this is a +ve quantity.

Now what would you say if I told you I completely disregarded that M^2. And then did the entire thing without it. would you say I am thick?

I'd say you lose one, maybe two marks