Answer:
see explanation
Explanation:
Given
p(x) = 2x² - 3x + 7
with a = 2, b = - 3, c = 7
If α and β are the zeros, then
the sum of the roots
α + β = -
=
←
and the product of the roots
αβ =
=
←
(a)
α² + β² = (α + β)² - 2αβ = (
)² - 2 ×
=
- 7 = -

------------------------------------------------------------------------------------------
(b)
α³ + β³
= (α + β)³ - 3α²β - 3αβ²
= (α + β)³ - 3α(α + β)
= (
)³ - 3 ×
×

=
-
= -

-----------------------------------------------------------------------------------------------
(c)
+

=

=
×
=
