Question

if alpha and beta are the zeroes of the quadratic polynomial f(x)=4x^2-5x-1,then find the value of 1/alpha + 1/beta?
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Answer 1

Answer:

-  5

Step-by-step explanation:

In a quadratic equation, ax^2 + bx + c,   sum S of roots is given by - b/a   and product P of roots is c/a.

In this equation,

S = α + β = -(-5/4) = 5/4

P = αβ = - 1/4

 Hence,

⇒ 1/α + 1/β

⇒ (β + α)/αβ

⇒ (5/4)/(-1/4)

⇒ 5/(-1)

⇒ - 5

Answer 2

Answer:

1/α + 1/β = -5

Step-by-step explanation:

Given that,

• Quadratic polynomial f(x) = 4x² - 5x - 1.

On comparing with ax² + bx + c : We get,

=> a = 4 , b = -5 , c = -1

Given that,

• α and β are zeroes of the polynomial.

=> Sum of roots = -b/a

=> α + β = -(-5)/4

=> α + β = 5/4

=> Product of roots = c/a

=> αβ = -1/4

Hence,

=> 1/α + 1/β

=> α+β/αβ

=> 5/4 / -1/4

=> 5/(-1)

=> -5

.°. 1/α + 1/β = -5.