Question

Find the polynomial whose sum and product of the zeros are -½ and ½ respectively.​

Answer 1

Step-by-step explanation:

Alpha = -1/2

Beta = 1/2

By using quadratic polynomial

x^2-(alpha+ beta)x+alphabeta

x^2-(-1/2+1/2)x + (-1/2) (1/2)

x^2-0.x-0.25

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Answer 2

Answer:

Sum of the zeroes = -1/2

i. e., alpha + beta = -1/2

Product of zeroes = 1/2

i. e., alpha × beta = 1/2

Then the polynomial is of the form

x² - (alpha + beta ) x + (alpha × beta ) = 0

x² - (-1/2) x + 1/2 = 0

x² + 1/2 × x + 1/2 = 0

x² + x/2 + 1/2 = 0

2x² + x + 1/2 = 0

2x² + x + 1 = 0

Then the polynomial is 2x² + x + 1

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