Let α, β, γ be the three  roots of the equation x3+bx+c=0 if βγ=1=−α then b3+2c3−3α3−6β3−8γ3 is equal to

Suppose that α, β and γ are the roots of the cubic equationx3 − 4x2 + 3x + 1 = 0.

Find all the roots α, β, γ of the cubicequation 3 7 6 0x x− − = . Also, find theequation whose roots are α + β, β + γand α + γ

For example if  α, β, γ  are roots of  ax3 + bx2 + cx + d  =  0 to find equation whose roots are  1/α, 1/β, 1/γ, we put  1α  =  y  ⇒  α  =  1y . As  α  is a root of  ax3 + bx2 + cx + d  =  0, we get  ay3 + by2 + cy + d  =  0  or  a + by + cy2 + dy3  =  0 This is the desired equation.The same result holds for all polynomial equations.If  α, β  are roots of  ax2 + bx + c  =  0  the roots of  a(x − 1)2 + b(x − 1)(x − 2) + c(x − 2)2  =  0  are

For α,β,γ≠0. If sin−1α+sin−1β+sin−1γ=π and (α+β+γ)(α−γ+β)=3αβ, then γ equal to

Input values of a,b,c for a quadratic equation and find roots of the equation..