Question

4.If a and ß are the roots of the equation
x2 - 2x + 4 = 0 then the value of a6 + B6 is:-
a) 64 b) 128 c) 256 d) none of these​

Answer 1

Answer:(A) 64

Step-by-step explanation:

comparing equation x2+2x+4=0 with ax2+bx+c=0 we get,

a=1 ; b=2 ; c=4

a + B = - b/a

a + B = - 2/1

a + B = -2

a6 + B6 = (-2)6

a6 + B6 = 64

Answer 2

d) none of these

explanation:

given equation: x²-2x+4=0

we know that α+β= -b/a

                               = 2

and αβ=c/a

            = 4

so,

(α+β)²=α²+β²+αβ

(2)²=α²+β²+4

4=α²+β²+4

4-4=α²+β²

0=α²+β²

α6+β6= (α²)³+(β²)³

        we know that a³+b³= (a+b)(a²-ab+b²)

α6+β6= (α²+β²)(α4-α²β²+β4)

          = 0