Question

The equation 2x^2-x+2=0 has roots a and B. Find the value of
a^3+B^3.

Answer 1

Assuming a and B are real solutions

Then a+B = -b/a = --1/2 = 1/2
and
a*B = c/a = 2/2 = 1

Answer 2

we know that, the sum of roots of a quadratic eq. is given by -
A+B = -b/a
so, here, A+B = 1/2
And, Products of roots = c/a = 2/2 = 1

Now ,\[A^{3}+B^{3} = (A+B)^{3}-3AB(A+B)\]
putting the values,
\[A^{3}+B^{3} = (1/2)^{3}-3(1)(1/2)\]
\[A^{3}+B^{3} = (1/8-3/2)\]
\[A^{3}+B^{3} = -11/8\]

Answer 3

Meh, everyone, stop typing faster than me :(