Question

If a & B are the zeroes of the quadratic polynomial p(x) = 3x - 5x+7, then find the
Svalue
of alpha ^2+beeta^2​

Answer 1

Answer:

Given expression,3x^2+5x+7

let it be equal to zero

3x^2+5x+7=0

here, a=3;b=5;c=7

The value of x is,

x=[-b±√b^2–4ac]/2a

x=[-5±√25–84]/6

x=[-5±√-59]/6

x=[-5± i √59]/6………………………………………….where i is the imaginary number{i=√-1}

x=[-5+i√59]/6 , x=[-5-i√59]/6

therefore; α=[-5+i√59]/6 ; β=[-5-i√59]/6

α^3=[-125 -i 59√59+i15√59(i√59–5)]\6……………………………….{i^3=-i}

Therefore,(α^3)+1=[-119 -i 59√59+i15√59(i√59–5)]\6

β^3=[-125 -i 59√59+i15√59(i√59+5)]\6