How to find the common root between two quadratic equations?

Hi evryone,

Am a beginner to Matlab,m trying to find out the common root between two quadratic equations of same variable x..plzz tell me how to do it. Plzz help!

Answer 1

[Matt J]

The ROOTS command should let you find and compare the roots of the 2 quadratics.

[roro6992]

But in dis case I need to find common root within a function whr I cnnt see d roots n compare by myslf. Is dere any method for directly finding d common root?? Plzz reply!

[Matt J]

Using the ROOTS command you can see the roots.

Answer 2

[Walter Roberson]

Let the two equations be of the form

a1*x^2+b1*x+c1 = 0
a2*x^2+b2*x+c2 = 0

then if

(1/4)*a2*b1^2/a^2+(-(1/2)*b2/a+(1/2)*a2*(b1^2-4*a1*c1)^(1/2)/a^2)*b1+(1/4)*a2*(b1^2-4*a1*c1)/a^2+c2-(1/2)*b2*(b1^2-4*a1*c1)^(1/2)/a

is 0, then the common root is

(-b1-sqrt(b1^2-4*a1*c1))/(2*a)

and otherwise the common root is

(-b1+sqrt(b1^2-4*a1*c1))/(2*a)

Provided, that is, that there really is a common root.