Question

Find a quadratic polynomial whose zeroes are 5+ root2 and 5-root2

Answer 1

Answer:

Step-by-step explanation:

Alpha = 5+/2. , beta = 5-/2

Alpha + beta = 5+/2+5-/2

= 10

Alpha. Beta = (5+/2)(5-/2)

= (5)²-(/2)²

=25-2 = 23

Eq = x²-(alpha + beta) x + alpha. Beta

= x²-10x+23

Hope it works

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Answer 2

Since, roots are 5-2^1/2 and 5+2^1/2

Therefore, quadratic equation is:-

[X+(5+2^1/2)]*[X-(5-2^1/2)]

X^2 -X(5-2^1/2) +X(5-2^1/2) -(5-2^1/2)*(5+2^1/2)

X^2 -5X + (2^1/2)X +5X -(2^1/2)X - 25 -5*2^1/2 -5*2^1/2 -2

X^2-10*2^1/2-2 :- answer.