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If alpha and beta are the zeroes of the polynomial f(x) = x^2 - x -4 find the value of 1/alpha + 1/beta - alpha*betapls answer fast ........................................its urgentpls ans asap

Answer»

Answer:

15 / 4

Step-by-step EXPLANATION:

Polynomials WRITTEN in the form of x^2 - Sx + P REPRESENT S as sum of their roots and P as product of their roots.

 Here, POLYNOMIAL is x^2 - x - 4

So S = 1 and P = - 4

  P = αβ = - 4

S = sum of roots = 1

  ⇒ α + β = 1

 In QUESTION :

⇒ 1 / α + 1 / β - αβ

⇒ ( β + α ) / αβ  -  αβ

⇒ ( sum of roots / product of roots ) - product of roots

⇒ ( 1 / - 4 ) - ( - 4 )

⇒- 1 / 4 + 4

⇒ ( - 1 + 16 ) / 4

⇒ 15 / 4


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