Number and sign

**dhiab** · July 24th 2009, 09:32 AM

m is the real parameter.
Find the real number and sign for the equation :

By two methods : graphic , algebric.

**J.R** · July 24th 2009, 10:38 AM

solve the equation in $\mathbb{C}$ perhaps ?

x^2+6x+9m=0

$\delta=36(1-m)$

talk about the sign.

for m>1 , m=1, m<1

**dhiab** · July 24th 2009, 11:59 AM

Originally Posted by J.R

solve the equation in $\mathbb{C}$ perhaps ?

x^2+6x+9m=0

$\delta=36(1-m)$

talk about the sign.

for m>1 , m=1, m<1

Hello : Thank you this equation in R

**J.R** · July 24th 2009, 11:23 PM

so what happened when m<1 ?

m=1 ?

and m>1 ?

**red_dog** · July 25th 2009, 12:17 AM

Graphic.

We have $m=-\frac{1}{9}x^2-\frac{2}{3}x$

Intersect the graph of $f(x)=-\frac{1}{9}x^2-\frac{2}{3}x$ with parallel lines to x-axis with equation $y=m$

If $m>1$ then the line doesn't intersect the graph.

If $m=1$ the line is tangent to the graph and the equation has a double solution $x=-3$

If $m\in(0,1)$ the line intersects the graph in 2 points and the equation has two negative solutions.

If $m=0$ then the equation has the solutions $x_1=-6, \ x_2=0$

If $m<0$ then the equation has one negative solution and one positive solution.

**dhiab** · July 25th 2009, 03:53 AM

Originally Posted by red_dog

Graphic.

We have $m=-\frac{1}{9}x^2-\frac{2}{3}x$

Intersect the graph of $f(x)=-\frac{1}{9}x^2-\frac{2}{3}x$ with parallel lines to x-axis with equation $y=m$

If $m>1$ then the line doesn't intersect the graph.

If $m=1$ the line is tangent to the graph and the equation has a double solution $x=-3$

If $m\in(0,1)$ the line intersects the graph in 2 points and the equation has two negative solutions.

If $m=0$ then the equation has the solutions $x_1=-6, \ x_2=0$

If $m<0$ then the equation has one negative solution and one positive solution.

HELLO : ALGEBRIC SOLUTION
Student sign of : delta , p=x1 ×x2 and s=x1 + x 2

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