+26367 Wie lauten die Nullstelle der Funktion f(x)= x^2 -5x + 4 ?
\(\begin{array}{rcll} \boxed{~ \begin{array}{rcl} ax^2+bx+c&=&0\\ x &=& {-b \pm \sqrt{b^2-4ac} \over 2a} \\ \end{array} ~}\\ f(x)&=& x^2 -5x + 4 \\ x^2 -5x + 4 &=& 0 \qquad & | \qquad a=1 \quad b=-5 \quad c = 4\\ x_{1,2} &=& {5 \pm \sqrt{5^2-4\cdot 1 \cdot 4} \over 2\cdot 1}\\ x_{1,2} &=& {5 \pm \sqrt{25-16} \over 2}\\ x_{1,2} &=& {5 \pm \sqrt{9} \over 2}\\ x_{1,2} &=& {5 \pm 3 \over 2}\\\\ x_1 &=& {5 + 3 \over 2}\\ x_1 &=& {8 \over 2}\\ x_1 &=& 4\\\\ x_2 &=& {5 - 3 \over 2}\\ x_2 &=& {2 \over 2}\\ x_2 &=& 1\\\\ \begin{array}{rcl} x = 4 \qquad \text{und} \qquad x = 1 \end{array} \end{array}\)
Die Nullstellen sind x = 1 und x = 4
+26367 Wie lauten die Nullstelle der Funktion f(x)= x^2 -5x + 4 ?
\(\begin{array}{rcll} \boxed{~ \begin{array}{rcl} ax^2+bx+c&=&0\\ x &=& {-b \pm \sqrt{b^2-4ac} \over 2a} \\ \end{array} ~}\\ f(x)&=& x^2 -5x + 4 \\ x^2 -5x + 4 &=& 0 \qquad & | \qquad a=1 \quad b=-5 \quad c = 4\\ x_{1,2} &=& {5 \pm \sqrt{5^2-4\cdot 1 \cdot 4} \over 2\cdot 1}\\ x_{1,2} &=& {5 \pm \sqrt{25-16} \over 2}\\ x_{1,2} &=& {5 \pm \sqrt{9} \over 2}\\ x_{1,2} &=& {5 \pm 3 \over 2}\\\\ x_1 &=& {5 + 3 \over 2}\\ x_1 &=& {8 \over 2}\\ x_1 &=& 4\\\\ x_2 &=& {5 - 3 \over 2}\\ x_2 &=& {2 \over 2}\\ x_2 &=& 1\\\\ \begin{array}{rcl} x = 4 \qquad \text{und} \qquad x = 1 \end{array} \end{array}\)
Die Nullstellen sind x = 1 und x = 4
!
