Question

Find a quadratic polynomial, the sum and product of whose zeroes are √2 -3/2

respectively. Also, find its zeroes​

Answer 1

Any quadratic equation can be written as:

x^2 -(sum of roots)x +(product of roots).

And it is also given that, sum of roots = √2 - 3/2

also, product of roots = √2 - 3/2

Therefore,

Equation becomes:

x^2 - (√2 - 3/2)x + √2 - 3/2

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Answer 2

Step-by-step explanation:

Quadratic polynomial is

x² - (alpha+Beta)x + (alpha*beta) = 0

x² - √2x + (-3/2) = 0

2x² - 2√2x - 3 = 0

alpha - Beta = √2 -4(-3/2)

= √(2+6) = √8 = 2√2

alpha + Beta = √2

2alpha = 3√2

alpha = 3/√2

beta = √2 - 3/√2 = -1/√2