Question

If alpha and beta are the zeroes of the quadratic polynomial f(x) = x2 - px + q, prove that alpha2/beta2 + beta2/alpha2= p4/q2 - 4p2/q + 2?​

Answer 1

Answer:

have, f(x)=x

2

−px+q

Since α and β are zeros of the given polynomial, then

α+β=

coefficient of x

2

−coefficient of x

=

1

−(−p)

=p ...(i)

Also, αβ=

coefficient of x

2

−constant term

=

1

q

=q ...(ii)

Now,

β

2

α

2

+

α

2

β

2

=

(αβ)

2

α

4

+β

4

=

(αβ)

2

(α

2

+β

2

)

2

−2α

2

β

2

=

(αβ)

2

[(α+β)

2

−2αβ]

2

−2

Answer 2

Step-by-step explanation:

sin square theta + cos square theta =1