Question

find a quadratic Plynomial each with the given numbers as the sum and product of its zeroes respectively -3/2√5, -1/2​

Answer 1

Answer:

Let the zeroes of the polynomial are alpha and beta.

alpha + beta = -3/2√5

alpha × beta = - 1/2

Then the polynomial is of the form,

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

x² - (-3/2√5 ) x + (-1/2) = 0

x² + 3/2√5 × x - 1/2 = 0

x² + 3x/2√5 - 1/2 = 0

2√5x²/2√5 + 3x/2√5 - √5/2√5 = 0

2√5x² + 3x - √5 = 0

Then the polynomial be 2√5x² + 3x - √5

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