if a and b are the zeroes of the quadratic polynomial f(x)=x^2-5x+4,find the value of 1/a+1/b-2ab

Question

mathslover · Answer

Remember this : 

$x^2 - \left(\text{Sum of zeroes}\right) x + \left(\text{Product of zeroes}\right) = 0 $ 

That is if you are given with a polynomial P(x) such that : 

$P(x) = x^2 - 5x + 4 =0 $ 

Then, 

5 = Sum of zeroes
4 = Product of Zeroes

mathslover · Answer

So, if the zeroes are : a and b

then

5 = a + b 
4 = ab

You have to find : $\cfrac{1}{a} + \cfrac{1}{b} -2ab$ 

Simplify this first : 

$\left( \cfrac{b + a}{ab} \right) -2ab$ 

Now, you know that a + b = 5 and ab = 4

Put the values and find the answer.

anonymous · Answer

thanks but can u solve and write the answer?

mathslover · Answer

@pritritis , on OpenStudy, we aim to help the users and not give them answers. You just have to put the values in and then you will get your answer. Where are you stuck? Give it some try.

anonymous · Answer

my answer is 27/4 just check if it is right?

mathslover · Answer

No! That's not right.

How did you calculate that?

anonymous · Answer

5/4-8
5-32/4

mathslover · Answer

5 -32 = ?