Question

if alpha and beta are the zeros of the polynomial FX equal to x square minus 1 then find a quadratic polynomial whose zeros are 2 alpha divided by beta and 2 Beta divided by Alpha​

Answer 1

Answer:

f(x) = x²-1

a = 1

b = 0

c = -1

α + β = -b/a = 0/1 = 0

=> α = -β

αβ = c/a = -1/1 = -1

=> (-β)(β) = -1

=> -β² = -1

=> β = 1

=> α = -1

new polynomial zeroes are:

2α/β = -2/1 = -2

and 2β/α = 1/-1 = -1

-2 - 1 = -b/a

=> -3 = -b/a

let a = 1

then, b = 3

-2 * 1 = c/a

=> -2 = c/1

=> c = -2

now we have all the coefficients

p(y) = 1y³ + 3y² -2

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