# I need help with an inequality question

1. Oct 2, 2004

### Gughanath

what are the range of values of k that gives the equation (k+1)x^2+4kx+9=0 ...I work it out ...please help

2. Oct 2, 2004

### arildno

Welcome to PF!
I think you have omitted something from your text; what was that?

3. Oct 2, 2004

### Gughanath

ups sorry...it should say at the end...that gives the equation no real roots

4. Oct 2, 2004

### arildno

And what do you think that means?

5. Oct 2, 2004

### shmoe

Hi, you can use the quadratic formula to find the roots of your equation. Forcing no real roots is equivalent to forcing the discriminant (the part under the root sign) to be negative. This will give you conditions on k that you're looking for.

ps. you have to make a restriction on k to guarantee that your equation is a quadratic and not linear. what is this restriction?

6. Oct 2, 2004

### Gughanath

i cant use the quadrativ formula for this euqation..when i work out the bracket i get

7. Oct 2, 2004

### arildno

Let a=k+1, b=4k, c=9.
ax^2+bx+c=0
Can you solve that one?

8. Oct 2, 2004

### Gughanath

i know that the discrimiant has to be smaller than 0....

9. Oct 2, 2004

### arildno

And what is the discriminant, expressed with a,b and c?

10. Oct 2, 2004

### Gughanath

no i am still confused

11. Oct 2, 2004

### arildno

12. Oct 2, 2004

### Gughanath

could you please just show me how i work out this questions?

13. Oct 2, 2004

### Gughanath

because then i will undertand

14. Oct 2, 2004

### arildno

Given the equation:
ax^2+bx+c=0
What is the discriminant?

15. Oct 2, 2004

### Gughanath

16k^2-(4[k+1]*9)<0 that becomes 16k^2-36k-36<0

16. Oct 2, 2004

### shmoe

Good, now can you find the values of k that satisfy this new inequality?

17. Oct 2, 2004

### arildno

Very good!
Here's a hint:
In order to find the range of k-values your after,
1. find the zeros in your discriminant.
That is, solve the equation for k:
$$16k^{2}-36k-36=0$$
2. You weren't interested in the k-values for which the discriminant was zero, but the k-values for which the discriminant is less than zero.
But you should figure out for yourself that those values must lie between the two values found in 1.

18. Oct 2, 2004

### Gughanath

i see that i have to factoris ethe equation in the disriminant now..but i cant find the right numbers

19. Oct 2, 2004

### arildno

Quite true!
Look at my previous post for hints.

20. Oct 2, 2004

### Gughanath

please...i have no idea how to continue...