Question

find the zeros of the quadratic polynomial X square + 7 x + 10 and verify the relationship between the zeros and the coefficient​

Answer 1

I hope this answer will help you

Answer 2

If alpha and beta are zeroes of polynomial x^2-bx+c=0, then how do I find the value of alpha^3+beta^3?

X^2-bx+c=0

Compare to the equation

a(x^2)+bx+c=0

So a=1,b=-b ,c=c

Alpha= [-b+((b^2)-4ac)^(1/2)]/2a

Alpha=[b+((b^2)-4c)^(1/2)]/2

Alpha^3=[[b+((b^2)-4c)^(1/2)]^3]/8

Alpha^3=(1/8)[b^3 +3(b^2)((b^2)-4c)^(1/2) +3b(b^2 - 4c) + ((b^2)-4c)^(3/2)]

Beta=[b-((b^2)-4c)^(1/2)]/2

Beta^3=[[b-((b^2)-4c)^(1/2)]^3]/8

Beta^3=(1/8)[b^3 -3(b^2)((b^2)-4c)^(1/2) +3b(b^2 - 4c) -((b^2)-4c)^(3/2)]

Alpha^3 + beta^3 =

(1/4)[b^3 +3b(b^2 - 4c) ]

=(1/4)(b^3 +3b^3 -12bc)

=(1/4)(4(b^3 - 3bc))

Alpha^3 + beta*3 = b(b^2 - 3c)