Question

find the quadratic polynomial whose zeroes are √2+3 and √2-3​

Answer 1

Answer:

$\huge\red{\boxed{\sf AnSwEr}}$

Let the Zeroes be

$\alpha \: and \: \beta$

we know that a Quadratic Equation is of form

$\huge\blue{\boxed{\sf x²+(sum of roots)x+product of roots }}$

Put the values

x²+(√2+3+√2-3)x+(√2+3)(√2-3)

x²+(2√2)x+(√2)²-(3)²

Quadratic Equation

$\huge\orange{\boxed{\sf x²+2√2x-7}}$

Answer 2

Alpha = root2 +3
Beta = root2-3
Sum of roots (alpha + beta)
= root2 + 3 + root2-3
= 2 root2

Product of roots (alpha*beta)
= (root2 + 3)(root2-3)
= [(root2)^2 - (3)^2]
= 2-9
= -7
x^2-Sx+P
x^2 -2root2x -7

So, the quadratic polynomial is
x^2 -2root2x -7.

Hope it will help you.
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