Question

If α and β are the zeros of the quadratic polynomial f(x) = 6x²+x-2, then the value of

1. α²+β²
2. 1/α+1/β​

Can Someone Answer This Quick Thank You <3​

Answer 1

Hi,

Explanation:

f(x)=6x²+x-2=6(x²+1/6*x-1/3)

`\alpha+\beta=(-1)/(6) \Longrightarrow\ (\alpha+\beta)^2=(1)/(36) \\\\\alpha*\beta=(-1)/(3) \\\alpha^2+\beta^2=(\alpha+\beta)^2-2\alpha*\beta=(1)/(36)+(2)/(3)=\boxed{(25)/(36)} \\\\(1)/(\alpha) +(1)/(\beta) =(\alpha+\beta)/(\alpha*\beta) =((-1)/(6) )/((-1)/(3) ) =(-1)/(6)*(-3)/(1)=\boxed{(1)/(2) }\\`

Answer 2

x=0.5 and x=-2/3

(0.5)^2+(2/3)^2 = 25/35
1/(0.5)+1/(2/3) = 3.5 or 7/2