Question

if α and β are the zeroes of the polynomial p(x)=2x^2-3x+7, evaluate:1/α +1/β and 1/2α-3+1/2β-3

Answer 1

ANSWER

2x

2

+3x+7=0

α+β=

2

−3

αβ=

2

7

Sum of zeros =

α

2

1

+

β

2

1

=

α

2

β

2

α

2

+β

2

=

(αβ)

2

(α+β)

2

−2αβ

=

(

2

7

)

2

(

2

−3

)

2

−(2×

2

7

)

2

=

4

49

4

9

−7

=−

49

18

Product of zeros =

α

2

β

2

1

=

(

2

7

)

2

1

=

49

4

∴ The polynomial is as follows:

x

2

+(

49

18

)x+

49

4

=0

∴49x

2

+18x+4=0

Answer 2

$\huge \star \underline \mathfrak \red{Answer }$

  α  and β  are    zeros / roots of   2 x² - 3 x + 7

        So  the sum of the roots = α + β =  - (-3/2) = 1.5 and   

              the product of the roots = α β =  7 / 2  = 3.5

$\begin{gathered}\frac{1}{\alpha}+\frac{1}{\beta}\\\\=\frac{\alpha+\beta}{\alpha \beta}\\\\=\frac{1.5}{3.5}=\frac{3}{7}\end{gathered}α1+β1=αβα+β=3.51.5=73</p><p>$

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