Real Roots Q (1 Viewer)

[Smile12345]

Hello All...

Could someone please help me with this Q?

Q. Find values of k in the equation

x^2 + (k + 1)x + (k+1/4) = 0 if:

the roots are real.
_______

So this means the discriminant is greater than or equal to 0??

Thanks in advance.

 

[asianese]

That's correct. Think of the quadratic formula:



The nature of the roots depend on the discriminant - if the roots are real, what's the restriction on the discriminant? Greater than or equal to 0.

 

[Smile12345]

That's correct. Think of the quadratic formula:



The nature of the roots depend on the discriminant - if the roots are real, what's the restriction on the discriminant? Greater than or equal to 0.

Good... Thanks (again)...

So will need to expand out (k + 1)^2 - 4 x 1 x (k+1/4)... This right?

 

[Smile12345]

Can someone please confirm I need to expand ... Then I should get k??

 

[asianese]

Expand that and make it greater or equal to 0.

 

[Smile12345]

Expand that and make it greater or equal to 0.

Yup, will do.. Thanks again.

 

[Smile12345]

Can someone help me expand the equation and make it greater than or equal to zero? Please?

Thanks in advance.

 

[Sy123]

So we need to find the values of k so that:









Its up to you to solve this inequality now

 

[Smile12345]

So we need to find the values of k so that:









Its up to you to solve this inequality now

Thanks heaps.... Is it the same if its (k + 1)/4

Sorry... I wrote it unclear.

 

[Sy123]

Thanks heaps.... Is it the same if its (k + 1)/4

Sorry... I wrote it unclear.

Oh if the co-efficient was ((k+1)/4) it woudl be:





We can either expand and simplify, or we can take the common factor (k+1)





Then you solve for the inequality =)

 

[Smile12345]

Oh if the co-efficient was ((k+1)/4) it woudl be:





We can either expand and simplify, or we can take the common factor (k+1)





Then you solve for the inequality =)

Ah ha... Thanks heaps.. .

Yup, I can....

 

[Smile12345]

How about

Find the exact values of p in the equation x^2 + px + 3 = 0 if
a) the roots are equal?
b) the roots are reciprocals of one another?

 

[Sy123]

How about

Find the exact values of p in the equation x^2 + px + 3 = 0 if
a) the roots are equal?
b) the roots are reciprocals of one another?

Use the facts that for some general quadratic equation:







How did I figure out to use these formula? Looking at the question its talking specifically about the roots of the quadratic equation IN RELATION to its co-efficients, the concept of this is explored in the formula.

So you just use those formula then to find p

 

[RealiseNothing]

How about

Find the exact values of p in the equation x^2 + px + 3 = 0 if
a) the roots are equal?
b) the roots are reciprocals of one another?

...

 

[Smile12345]

Thanks for your comments Sy...

I will continue to work on this....

 

[Smile12345]

Thanks for your helpful hint... 'Realise Nothing'

 

[levaly]

You can also check out this step by step solution:

http://www.symbolab.com/solutions/quadratic_equations?query=x^{2} + (k + 1)x + (k+1/4) = 0

 

[Smile12345]

You can also check out this step by step solution:

http://www.symbolab.com/solutions/quadratic_equations?query=x^{2} + (k + 1)x + (k+1/4) = 0

Thanks heaps... Appreciate that.