Question

If alpha and beta are the zeros of the polynomial p(x)=x2-5x+2.

Find, 1/alpha
Find, 1/beta

Find, 1/alpha+1/beta=3×alpha×beta

Answer 1

Answer:

1/α  + 1/β = 5/2

3αβ  = 6

1/α  , 1/β = (5± √17)/4

Step-by-step explanation:

alpha and beta are the zeros of the polynomial p(x)=x2-5x+2.

x² - 5x + 2

Sum of Zeroes = -b/a

Products of Zeroes = c/a

a = 1  b = -5  c = 2

Zeroes are α  & β

α + β = 5

αβ = 2

1/α  + 1/β

= (β  + α)/αβ

= 5/2

1/αβ  =  1/2

x² - 5x/2  + 1/2 = 0

=> 2x² - 5x + 1 = 0  where zeroes are 1/α  & 1/β

1/α  & 1/β = (5 ± √25 - 8)/4   =  (5± √17)/4

3αβ  = 3*2 = 6

Answer 2

alpha and beta are the zeros of the polynomial p(x)=x2-5x+2.

x² - 5x + 2

Sum of Zeroes = -b/a

Products of Zeroes = c/a

a = 1 b = -5 c = 2

Zeroes are a & ß

a +3=5

αβ = 21/a + 1/3

= (B + a)/aß

= 5/2

1/αβ = 1/2

x² - 5x/2 + 1/2 = 0

=> 2x² - 5x+1=0

where zeroes are 1/a & 1/3

1/a & 1/B = (5 ± √25 - 8)/4

=

(5± √17)/4

3aß =3*2= 6