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

Answer:see explanationStep-by-step explanation:Givenp(x) = 2x² - 3x + 7with a = 2, b = - 3, c = 7If α and β are the zeros, thenthe sum of the rootsα + β = - [tex]\frac{-3}{2}[/tex] = [tex]\frac{3}{2}[/tex] ← and the product of the rootsαβ = [tex]\frac{c}{a}[/tex] = [tex]\frac{7}{2}[/tex] ←(a)α² + β² = (α + β)² - 2αβ = ([tex]\frac{3}{2}[/tex] )² - 2 × [tex]\frac{7}{2}[/tex] = [tex]\frac{9}{4}[/tex] - 7 = - [tex]\frac{19}{4}[/tex]------------------------------------------------------------------------------------------(b)α³ + β³= (α + β)³ - 3α²β - 3αβ² = (α + β)³ - 3α(α + β)= ([tex]\frac{3}{2}[/tex] )³ - 3 × [tex]\frac{7}{2}[/tex] × [tex]\frac{3}{2}[/tex]= [tex]\frac{27}{8}[/tex] - [tex]\frac{63}{4}[/tex] = - [tex]\frac{99}{8}[/tex]-----------------------------------------------------------------------------------------------(c)[tex]\frac{1}{\alpha }[/tex] + [tex]\frac{1}{\beta }[/tex]= [tex]\frac{\alpha+\beta  }{\alpha\beta  }[/tex]= [tex]\frac{3}{2}[/tex] × [tex]\frac{2}{7}[/tex] = [tex]\frac{3}{7}[/tex]