Question

Given that alpha and Beta are rout of 3x²-4x-1= 0; find a) Alpha + Beta b) Alpha Beta c) Alpha² + Beta² d) 1/alpha + 1/Beta​

Answer 1

Hi,

Explanation:

`f(x)=3x^2-4x-1=0\\\\\alpha + \beta =(4)/(3) \\\alpha * \beta=(-1)/(3) \\\\(\alpha + \beta)^2=\alpha^2 + \beta^2+2\alpha \beta\\\\\alpha^2 + \beta^2=(\alpha + \beta)^2-2\alpha \beta=((4)/(3)) ^2-2*(-1)/(3)\\=(16)/(9) +(6)/(9) \\\\=(22)/(9) \\\\\\(1)/(\alpha) +(1)/(\beta)\\=(\beta+\alpha)/(\alpha*\beta) \\\\=((4)/(3) )/((-1)/(3) ) \\\\=(4)/(3)*(3)/(-1) \\\\=-4\\`