Question

I a ,b are the zeroes of the polynomial x²+6x +2 then (1/a + 1/b )
​

Answer 1

Answer:

If a, b are zeros of polynomial 6x^2+x-1, then how do you find the value of a/b+b/a+2 (1/a+1/b)?

Amazon Prime Video - start a 30 day free trial.

Lemme tell you first, I don't know how to write math script in here. So bear with the equations I write okay?

The given equation can be divided by any number but the zeros of that polynomial will remain same. So dividing the equation by 6, we get :

x²+x/6–1/6 (Eqn I)

Now we know that :

(x-a)(x-b) = x²-(a+b)x+ab where a and b are the roots.

Comparing this to eqn I, a+b =-1/6 and ab =-1/6

Therefore a+b=ab, hence (a+b)/ab = 1/a+1/b =1 (eqn II)

now a/b+b/a = (a²+b²)/ab by just taking a common denominator.

a²+b² =(a+b)²-2ab =1/36-(-2/6)=13/36

Therefore (a²+b²)/ab =19/36÷(-1/6) =-13/6 (eqn III)

Finally (eqn III) + 2*(eqn II) = -13/6 + 2 =-1/6