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# help

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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

#1
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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

!

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