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

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

If α,β and γ are the zeroes of the polynomial f(x)=ax3+bx2+cx+d, then 1α+1β+1γ i

If  α, β  are zeros of  ax2 + bx + c, ac  ≠  0 , then zeros of  cx2 + bx + a  are Select an answerA −α, −β B α, 1β C β, 1α D 1α, 1β

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

Given that one of the zeroes of the cubic polynomial ax3 + bx2 + cx + d is one, the product of the other two zeroes isSelect an answerA–c/a         B–d/a     C0Dc/a