Question

If ∝ and β are the zeros of the polynomial f(x) = `6x^2 + x - 2 `find the value of `(∝/β+∝/β) ` 

 

Answer 1

By using the relationship between the zeroes of the quadratic polynomial.
We have 

Sum of zeroes=`(-("Coefficent of x"))/("Coefficient of" x^2)` and Product of zeroes = `"Constant term"/("Coefficient of" x^2)` 

∴ 𝛼 + 𝛽=`-1/6` and 𝛼𝛽 =`-1/3` 

Now, `∝/β+β/∝=(∝^2+β^2)/(∝β)` 

`= (∝^2+β^2+2∝β-2∝β)/(∝β)` 

`=((∝+β)^2-2∝β)/(∝β)` 

`=((-1/6)^2-2(1/3))/(1/3)` 

`=(1/36+2/3)/ (1/3)`   

`=-25/12`