Say I have 2 quadratics

p(x^2)+qx=r=0 and d(x^2)+ex+f=0with one common root

can i write (p/d)=(q/e)=(r/f) ?

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- Oct 31st 2013, 08:17 PMAaPaComparing coefficients in quadratic?
Say I have 2 quadratics

p(x^2)+qx=r=0 and d(x^2)+ex+f=0**with one common root**

can i write (p/d)=(q/e)=(r/f) ? - Oct 31st 2013, 08:31 PMtopsquarkRe: Comparing coefficients in quadratic?
- Oct 31st 2013, 10:43 PMAaPaRe: Comparing coefficients in quadratic?
no.

so when can we compare coefficients? - Oct 31st 2013, 10:46 PMSlipEternalRe: Comparing coefficients in quadratic?
If $\displaystyle p(x),q(x)$ are two polynomials with the exact same set of roots and the same degree, then $\displaystyle p(x) = kq(x)$ where $\displaystyle k$ is some constant. That is when you can compare coefficients.

- Nov 1st 2013, 02:18 AMAaPaRe: Comparing coefficients in quadratic?
All my confusions which troubled me have disappeared. You really made me think on my own.

**Thank you very very muchh!!** - Nov 1st 2013, 02:24 AMAaPaRe: Comparing coefficients in quadratic?
hey

like comparing coefficients.

can we compare exponents as in this given equation

[(a^n) + (b^n)]/[(a^n-1) + (b^n-1)] = (a+b)/2 (n-1 is exponent)

to get n=1

if yes then what is the condition that allows us to compare? - Nov 1st 2013, 10:03 PMAaPaRe: Comparing coefficients in quadratic?
[itex]a^n + b^n / a^n-1 +b^n-1 = a+b / 2[/itex]

- Nov 2nd 2013, 12:06 AMIdeaRe: Comparing coefficients in quadratic?
Maybe this will help

Two quadratic polynomials

$\displaystyle x^2 + b x + c$

$\displaystyle x^2 + s x + t$

have a root in common if and only if

$\displaystyle c^2 - b c s + c s^2 + b^2 t - 2 c t - b s t + t^2 = 0$ - Nov 2nd 2013, 04:26 AMAaPaRe: Comparing coefficients in quadratic?
$\displaystyle \frac {a^n + b^n} { a^{n-1} + b^{n-1}} = \frac{a+b} {2} $

by comparing exponents we get n=1

exactly when can we compare exponents like this? - Nov 2nd 2013, 05:42 AMtopsquarkRe: Comparing coefficients in quadratic?
Well...We can solve this in terms of a and b: b = -a for odd n, so there is no specific relationship needed for n. But generally we can match coefficients of terms on each side of an equation if the terms are members of an orthogonal series. The "power series" is such a series: $\displaystyle a_0 + a_1x + a_2 x^2 + ...$. Many other orthogonal expansions exist but you'll see the power series the most often.

-Dan - Nov 2nd 2013, 08:42 AMAaPaRe: Comparing coefficients in quadratic?
let us say that a and b are positive distinct real natural numbers....is there any other value of n that satisfies the equation? how do we tell?