Quadratic help

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

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?

Reply 1

mqb2766

Original post by sqrt123

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

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)

Reply 2

sqrt123

(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!!!

Reply 3

tonyiptony

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.