Question

if alpha and beta are the zeros of the polynomial 2x2 - 3x - 9 find the value of polynomial whose zeros are alpha + 1 and beta + 1

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Answer 1

The polynomial can be factored into: (x+1)(2x-5), so we have α = -1 and β = 5/2

(i) The polynomial with zeros α2 and β2 can be factored as (x - α2)(x - β2). This can be multiplied out to get

x2 - (α2 + β2)x + α2β2 or x2 - (1 + 25/4)x + 25/4 or x2 - (29/4)x + 25/4

Multiply all the terms by 4 to get 4x2 - 29x + 25

See if you can now do part (ii).

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Answer 2

Explanation:

2x²-(6-3)x-9

2x²-6x+3x-9

2x(x-3)+3(x-3)

(x-3)(2x+3)

here alpha is 3 and beta is -3 upon2

alpha+1= 3+1=4

beta+1= -1 upon2