If α and β be the two zeroes of the quadratic polynomial p(x) = 2x2 – 3x + 7. evaluate
a) α2 + β2 b) α3 + β3 c ) 1/ α+ 1/β

see explanation

Step-by-step 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 = -

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(b)

α³ + β³

= (α + β)³ - 3α²β - 3αβ²

= (α + β)³ - 3α(α + β)

= ( )³ - 3 × ×

= - = -

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(c)

+

=

= × =

reduce the friction between its moving parts

step-by-step explanation:

in fact, by reducing the friction between the moving parts of the machine, it is possible to reduce the energy wasted due to this friction; therefore, more input energy is converted into useful work, and this will improve the efficiency of the machine.