# Quadratic help

Hi, I am struggling with this question - could anyone help please?

Consider the equation 2x^2 + 4x + c = 0 where c is a constant.
The positive difference between the roots of this equation is sqrt10.
What is the value of c?
Original post by sqrt123
Hi, I am struggling with this question - could anyone help please?

Consider the equation 2x^2 + 4x + c = 0 where c is a constant.
The positive difference between the roots of this equation is sqrt10.
What is the value of c?

If you think about the quadratic formula, the roots are
-b/2a +/- sqrt|(...)/2a
Subtracting one from the other gives the difference and equating to sqrt(10) should give you an equation that you can solve.
(edited 7 months ago)
(Original post by mqb2766)If you think about the quadratic formula, the roots are
-b/2a +/- sqrt|(...)/2a
Subtracting one from the other gives the difference and equating to sqrt(10) should give you an equation that you can solve.

Brilliant, thank you!!!
Alternatively, without going through the kerfuffle of the quadratic formula, you can write down the sum of the roots being -2 (why?).

So now we know the sum of the two roots, and the difference of the two roots, which means it's just a matter of solving two equations in two unknowns.

EDIT: Yet another way along roughly the same line of thought
Note that (a-b)^2 = (a+b)^2 - 4ab.
In other words, we can rewrite the square of the difference of two roots in terms of the sum and product of the roots.

This "note that" is by experience - the more you do maths, the more likely you can spot it.
(edited 7 months ago)