Question

If α and β be the two zeroes of the quadratic polynomial P(x) = 2x2 – 3x + 7. Evaluate

Answer 1

Answer:

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 = - $\frac{-3}{2}$ = $\frac{3}{2}$ ←

and the product of the roots

αβ = $\frac{c}{a}$ = $\frac{7}{2}$ ←

(a)

α² + β² = (α + β)² - 2αβ = ($\frac{3}{2}$ )² - 2 × $\frac{7}{2}$ = $\frac{9}{4}$ - 7 = - $\frac{19}{4}$

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(b)

α³ + β³

= (α + β)³ - 3α²β - 3αβ²

= (α + β)³ - 3α(α + β)

= ($\frac{3}{2}$ )³ - 3 × $\frac{7}{2}$ × $\frac{3}{2}$

= $\frac{27}{8}$ - $\frac{63}{4}$ = - $\frac{99}{8}$

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(c)

$\frac{1}{\alpha }$ + $\frac{1}{\beta }$

= $\frac{\alpha+\beta }{\alpha\beta }$

= $\frac{3}{2}$ × $\frac{2}{7}$ = $\frac{3}{7}$