I with an inequality question

  • Thread starter Gughanath
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    Inequality
In summary: PIn summary, the range of values of k that gives the equation (k+1)x^2+4kx+9=0 no real roots is -3/4 < k < 3. This can be found by factoring the discriminant and setting it less than 0, resulting in the interval (-3/4, 3).
  • #1
Gughanath
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what are the range of values of k that gives the equation (k+1)x^2+4kx+9=0 ...I work it out :confused: ...please help
 
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  • #2
Welcome to PF!
I think you have omitted something from your text; what was that?
 
  • #3
ups sorry...it should say at the end...that gives the equation no real roots
 
  • #4
And what do you think that means?
 
  • #5
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
i can't use the quadrativ formula for this euqation..when i work out the bracket i get
x^2+x^2k+4kx+9=0 ...i have no idea how to use the discrimant in this case..please help
 
  • #7
Let a=k+1, b=4k, c=9.
Then your equation looks like
ax^2+bx+c=0
Can you solve that one?
 
  • #8
i know that the discrimiant has to be smaller than 0...
 
  • #9
And what is the discriminant, expressed with a,b and c?
 
  • #10
no i am still confused
 
  • #11
What is your problem?
 
  • #12
could you please just show me how i work out this questions?
 
  • #13
because then i will undertand
 
  • #14
I ask you again:
Given the equation:
ax^2+bx+c=0
What is the discriminant?
 
  • #15
16k^2-(4[k+1]*9)<0 that becomes 16k^2-36k-36<0
 
  • #16
Gughanath said:
16k^2-(4[k+1]*9)<0 that becomes 16k^2-36k-36<0

Good, now can you find the values of k that satisfy this new inequality?
 
  • #17
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:
[tex]16k^{2}-36k-36=0[/tex]
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
i see that i have to factoris ethe equation in the disriminant now..but i can't find the right numbers
 
  • #19
Gughanath said:
i see that i have to factoris ethe equation in the disriminant now..but i can't find the right numbers
Quite true!
Look at my previous post for hints.
 
  • #20
please...i have no idea how to continue...
 
  • #21
Well, what values of k solves:
[tex]16k^{2}-36k-36=0[/tex] ?

(Note: You were asked to find the values of k so that the discriminant is less than zero, not zero, but finding the zeroes is a good start)
 
  • #22
k..thanks for your help...
 
  • #23
Now, having found the k-values yielding zero discriminant, you should be able to write the discrimanant as:
[tex]16k^{2}-36k-36=16(k-3)(k+\frac{3}{4})[/tex]
What must then the k-interval be which yields negative discriminant?
 
  • #24
how did u factorise that?
 
  • #25
It is the roots of equation gained by setting the discriminant equal to 0 (that is, -3/4 and 3 are the roots)
 
  • #26
ooo (: I am so...now i undertand it...the discriminant is 16k^2+36k-36..simplified it becomes 16[k^2 - (9/4)k - 9/4]...-3 and +3/4 multiplied give -9/4 and when added they also give -9/4...so these are these are the roots..factorised the equation becomes 16[(k-3)(k+3/4)]=0..the values of k here is 3 or -3/4...but the equation must be lower than 0 for 16[(k-3)(k+3/4)]<0 the range of the values of k are in -3/4<k<3...is that right?
 
  • #27
thanks a lot for your help everyone...sorry for bothering you..i was so busy yesterday my brain wasant running properly...lol
 
  • #28
You're right about the interval;I wouldn't agree to what you said about your brain, though..
 
  • #29
very good so any k that satisfies 16k^2-36k-36<0 is the k we are looking for ..
lets divide throughout by 4 to make the eqn simple
we get 4k^2-9k-9<0
i can write this as,
(4k+1)(k-3)<0

what does this imply?
(Note : if x*y < 0 it means multiplication of x and y must be negative)

-- AI
 
  • #30
damn ! i did not realize this thread had 2 pages!
umm please delete my current and last post as they are totally irrelevant now!

-- AI
 
  • #31
In addition, it should be
(4k+3)(k-3)<0
Drown in shame..:wink:
 
  • #32
*drowns himself in a bowl of red wine*

-- AI
 
  • #33
TENALIRAMAN!
Are you still with us??
Get out of that bowl at once, I'm sorry I led you on to that! :cry:
 
  • #34
ssh arildno,
i am waiting for some baywatch girl to give me CPR

-- AI
 
  • #35
lol, it was all setup
 

1. What is an inequality?

An inequality is a mathematical statement that compares two quantities or expressions, typically using symbols such as <, >, ≤, or ≥. It indicates that one quantity is greater than or less than the other.

2. How do you solve an inequality?

To solve an inequality, you must isolate the variable on one side of the equation and simplify the other side. Remember to reverse the inequality sign if you multiply or divide by a negative number. The solution is typically expressed in interval notation or using a number line.

3. What is the difference between an equation and an inequality?

An equation is a statement that shows the equality of two expressions, while an inequality shows the relationship between two expressions, indicating that one is greater than or less than the other. In an equation, the two sides are equal, while in an inequality, the two sides are not necessarily equal.

4. Can you graph an inequality?

Yes, you can graph an inequality on a coordinate plane. The solution to an inequality is typically represented by a shaded region on the graph, with a solid or dashed boundary line depending on whether the inequality includes or excludes the boundary value.

5. How do you know if a point is a solution to an inequality?

To determine if a point is a solution to an inequality, you can substitute the values of the coordinates into the inequality and see if the statement is true. If the point satisfies the inequality, it is a solution. If not, it is not a solution.

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