Quadratic equation and roots HELP PLEASE!! (1 Viewer)

[samsonhohoho]

In the equation (c-2)x^2 - 5x + 2c + 3 = 0, the roots are reciprocals of each other. Find the value of c. Please help and show your working. Thanks

 

[RealiseNothing]

Product of roots:



But since they are reciprocals, they multiply together to obtain 1, hence:

 

[samsonhohoho]

the answer i found in the answer sheet is c = -5 !?

Product of roots:



But since they are reciprocals, they multiply together to obtain 1, hence:

 

[RealiseNothing]

the answer i found in the answer sheet is c = -5 !?

I did a typo. Check now.

 

[samsonhohoho]

it says the roots are d and 1 over d. I get this part but then it says

d*1/d = 2e+3 over (c-2) <-- i dont get this, maybe the syllabus changed and the teacher didnt teach us that

 

[RealiseNothing]

it says the roots are d and 1 over d. I get this part but then it says

d*1/d = 2e+3 over (c-2) <-- i dont get this, maybe the syllabus changed and the teacher didnt teach us that

Have you done the product of roots?

 

[samsonhohoho]

probably not, im in prelim this year

 

[Alkanes]

Basic polynomials is taught during prelim from memory.

 

[samsonhohoho]

I think the syllabus have changed

 

[RealiseNothing]

probably not

Ok well sums and products of roots 101 time:

Let's think of the general quadratic equation:



Now if we factorise this to find the roots, it looks like this:



Where

Now expand this:



If we consider the general equation again, we can make a relationship between the roots and co-efficients of a quadratic. However the above equation is monic, so we have to make the general equation monic as well by dividing by 'a':



Now if we equate the two expressions we have:



So if we equate the co-efficients of each side we get:



Which becomes:



Since alpha and beta are the sum of the roots, we can say that the sum of the roots is equal to

Like-wise:



Since alpha times beta is the product of the roots, we can say that the product of the roots is

 

[RealiseNothing]

I think the syllabus have changed

It hasn't changed.