Question

if alpha and beta are zeros of quadratic polynomial x square - 2 x minus 8 then find the value of one by Alpha Square oneplus One by beta square​

Answer 1

Answer:

quadratic polynomial whose zeros are 1 + α and 1 + β will be x² - 2x  - 4

Step-by-step explanation:

Given ,

x² - 5 = 0

=> (x-√5)(x + √5) = 0

=> x = ±√5

hence

α = √5 and β = -√5

new roots

= 1 + α  and 1  + β

= 1 + √5  and 1  - √5

hence the new equation will be

[x-(1+α)][x-(1+β)] = 0

=> [x-(1+√5)][x-(1-√5)] = 0

=> x² -(1+√5)x - (1-√5)x + (1+√5)(1-√5) = 0

=> x² - 2x + 1 - 5 = 0

=> x² - 2x  - 4 = 0

which is the required quadratic equation

Step-by-step explanation:

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Answer 2

x2-2x+4

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