Question

If alpha and beta are the zeroes of x2+5x+5then find alpha-1+beta-1

Answer 1

Answer:

Step-by-step explanation:

f α, β are the zeros of 2x + 5x + 5 find the value of α-1+β-1?

Given quadratic polynomial is p(x) = 2x+5x+5

Since α, β are zeroes of the given polynomial, we have

Sum of roots (α+ β) = − (b/a) = − (5/1) = −5

Product of roots (αβ) =  (c/a) = (5/1) = 5

Consider, α-1+β-1 = (1/ α) + (1/ β)

                                  = (α + β)/ αβ

                                  = (− 5 )/ 5 = −1

Answer 2

The correct answer is -1

Given that, $f(x) = x^2+ 5x + 5$

Comparing with the general form of polynomials, $ax^2 + bx + c = 0$,

⇒ a = 1 ,

   b= 5   and

   c = 5

The sum of the zeros = α + β = $\frac{-b}{a}$ = $\frac{-5}{1}$ = -5

The product of zeros =   β    =  $\frac{c}{a}$ =   $\frac{5}{1}$ = 5

Thus,   $\frac{1}{alpha} + \frac{1}{beta}$   =   $\frac{alpha + beta}{alpha beta}$  

                                 = $\frac{-5} { 5}$

                                 = -1

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