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Consider the system of quadratic equations

\(\begin{align*} y &=3x^2 - 5x, \\ y &= 2x^2 - x - c, \end{align*}\)

where c is a real number.

 

a) For what value(s) of c will the system have exactly one solution (x,y)?

b) For what value(s) of c will the system have more than one real solution?

c) For what value(s) of c will the system have no real solutions?

 Apr 7, 2020
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Consider the system of quadratic equations

\(\begin{align*} y &=3x^2 - 5x, \\ y &= 2x^2 - x - c, \end{align*} \)

where c is a real number.

 

a) For what value(s) of c will the system have exactly one solution (x,y)?

b) For what value(s) of c will the system have more than one real solution?

c) For what value(s) of c will the system have no real solutions?

 

Hello Guest!

 

Betrachten Sie das System der quadratischen Gleichungen
\(\begin{align*} y &=3x^2 - 5x, \\ y &= 2x^2 - x - c, \end{align*} \)
wobei c eine reelle Zahl ist.

a) Für welche Werte von c hat das System genau eine Lösung (x, y)?
b) Für welche Werte von c hat das System mehr als eine echte Lösung?
c) Für welche Werte von c hat das System keine wirklichen Lösungen?

 

\(3x^2-5x=2x^2-x-c\\ x^2-4x+c=0\)

 

\(x=-\frac{b}{2}\pm\sqrt{(\frac{b}{2})^2-c}\)

 

\(x=\frac{4}{2}\pm\sqrt{(\frac{4}{2})^2-c}\\ x=2\pm\sqrt{4-c}\\\)

 

a) c = 4    \(x=2\ ;\ y=2\)

b) \(-\infty\) < c < 4 

c) c > 4

laugh  !

 Apr 7, 2020
edited by asinus  Apr 7, 2020
edited by asinus  Apr 7, 2020
edited by asinus  Apr 7, 2020
edited by asinus  Apr 7, 2020

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