Question

if alpha and beta are zeroes of 5x^2+5x+1 then find value of alpha^-1 and beta ^-1​

Answer 1

Step-by-step explanation:

Given :

α and β are the zeroes of the polynomial 5x² + 5x + 1.

To find :

α⁻¹ + β⁻¹

Solution :

We have 5x² + 5x + 1,

Where :

• a = 5
• b = 5
• c = 1

Sum of zeroes :

》α + β = -b/a

• -5/1
• -1

Product of zeroes :

》α × β = c/a

• 1/5

α⁻¹ + β⁻¹ is nothing but 1/α + 1/β :

Taking L.C.M we get :

• (β + α)/(αβ)

Substituting the value,

• (-1)/(1/5)
• -5

∴ The value of α⁻¹ + β⁻¹ is -5.

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Answer 2

We have 5x² + 5x + 1,

Where :

a = 5

b = 5

c = 1

Sum of zeroes :

==> α + β = -b/a

-5/1

-1

Product of zeroes :

==>α × β = c/a

1/5

α⁻¹ + β⁻¹ is also 1/α + 1/β :

After taking lcm we get:-

(β + α)/(αβ)

Put the value ,we get:-

(-1)/(1/5)

-5

So the  value of α⁻¹ + β⁻¹ is -5.