Unknown roots of two quadratics

**BG5965** · July 9th 2009, 07:43 AM

Let $(a, c)$ and $(b, d)$ be the roots of the equation $x^2 + ax - b = 0$ and $x^2 + cx + d = 0$ respectively. Find all possible real values for $a, b, c, d$

I'm not sure how to do this question and not sure how to approach it.

Please help, BG

**Moo** · July 9th 2009, 07:52 AM

Hello,

In a quadratic equation $x^2+mx+n=0$ , m is the sum of the roots, and n is the product of the roots.

So from the second equation, we have $bd=d$ (1). And $c=b+d$ (2)
And from the first one, we have $ac=-b$ (3) and $a+c=a$ (4)

From (4), we get c=0
Substituting in (3), we get b=0
Substituting in (1), we get d=0

Then, a can take any values you want...

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