Question

If alpha and beta are the zeros of polynomial x2+4x+3 find the polynomial whose zeros are 1-beta/alpha and 1+alpha/beta

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

1-beta/alpha = √28/3 and 1+alpha/beta = -4/3

Step-by-step explanation:

Given that alpha and beta are the zeroes of the equation x²+4x+3

Thus, alpha+beta=-b/a = -4/1 -------(1)

Again, alpha.beta = c/a = 3

We have to find the value of 1-beta/alpha and 1+alpha/beta

We know that, (alpha - beta)² = (alpha + beta) -4 alpha.beta

Therefore, alpha - beta = √(alpha + beta) -4alpha.beta

Now, alpha-beta/alpha.beta = 1-beta/alpha

=> √(-4)²-(4)(3)/3

=> √16+12/3

=> √28/3

=> 1-beta/alpha = √28/3

=> 1+alpha/beta = alpha+beta/alpha.beta = -4/3

Therefore,

1-beta/alpha = √28/3 and 1+alpha/beta = -4/3

Hope I helped you