Question

if alpha and beta the product of two zeros of the polynomial p(x) 3x2-10x+7 find the value of alpha2 and beta2

Answer 1

In the given equation
The coefficenents of A,B,C are
3,-10,7 respectively

As we know that product of root =
Alpha x Beta = C/A

Alpha x Beta = 7/3..............(i)eq

and also we know that sum of roots =
Alpha + Beta = -B/A

Alpha + Beta =10/3

Alpha = 10/3 - Beta..............(ii)eq

Put Alpha in eq (i)

(10/3 - Beta ) x Beta = 7/3

10/3 Beta - Beta^2 = 7/3

Beta^2 - 10/3 Beta + 7/3 = 0

(multiply the equation by 3)

3 Beta^2 - 10 Beta +7=0

on solving the equation we get Beta=1
or
Beta=7/3

.....................

Now put Beta in equation (ii)

Alpha = 10/3 -1
Alpha= 7/3

or
Alpha=10/3-7/3
Alpha=1