is three time the other roots.Find the value of .

please help..i dont know how to do..(Crying)

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- May 24th 2010, 10:18 AMmastermin346quadratic equation problem
is three time the other roots.Find the value of .

please help..i dont know how to do..(Crying) - May 24th 2010, 10:33 AMDinkydoe
Can you be a little more specific?

Do you mean that if is a root, then the other root is ?

Then find the corresponding ? - May 24th 2010, 10:38 AMmastermin346
- May 24th 2010, 11:09 AMpapex
in that case, rewriting the equation as: x^2-4x+p-2=0 we have -4=4a and p-2=3a^2

thus a=-1 and p=5

the equation becomes x^2-4x+3=0 which has 1 and 3 as roots - May 24th 2010, 11:12 AMDinkydoe
Ok, write the equation as

Suppose that

Now we have and we can solve . - May 24th 2010, 11:28 AMArchie Meade
Hi mastermin346,

Factorising is the fastest way.

Here the sum of the roots=4.

One is 3 times the other, so the sum of the roots is 4 times the smaller root.

Smaller root = 4/4.

If you had an expression that was difficult to factorise,

you could proceed as follows.....

The solutions (roots) of a quadratic equation

are

One root is

The other root (a quadratic has at most 2 roots) is

First re-arrange your equation to

If one root is 3 times the other, the bigger root__must__be the one with the +

The denominator is common, so it is irrelevant.

This gives