Question

if alpha and beta are the zeroes of x2-4x+1 then 1÷alpha + 1÷beta -alpha×beta​

Answer 1

Answer:

3

Step-by-step explanation:

Given equation is $x^{2} - 4x + 1 = 0$

α and β are the zeroes of given equation.

⇒ 1/α + 1/β - α×β

⇒ (α + β - (αβ)^2)/αβ  (Here (αβ)^2 represents square of αβ)

The given equation is of the form $ax^{2} + bx + c = 0$.

If α and β are the zeroes of the above equation then

       α + β = -b/a  and   αβ = c/a

Here, a = 1, b = -4 and c = 1

      α + β = -(-4/1) = 4

       αβ = 1/1 = 1

⇒  (4 - 1^2)/1

⇒  4-1

⇒  3