Question

Form a polynomial whose zeroes are 2 + 1√2and 2 –1√2

Answer 1

Given:-

→α=2+1√2

→β=2-1√2

$\rule{200}{1}$

To Find:-

→ A Polynomial using Quadratic Formula?

$\rule{200}{1}$

AnsWer:-

•Using Quadratic Formula•

๛k[x²-(α+β)x+αβ]–(1)

→α+β=2+1√2+(2-1√2)

→α+β=4–(2)

→αβ=(2+1√2)×(2-1√2)

→αβ=4-2√2+2√2-2

→αβ=2–(3)

★Using (3)&(2) in (1)★

→k[x²-(4)x+2]

→k[x²-4x+2]

♦Let k=1♦

→1[x²-4x+2]

→x²-4x+2

๛x²-4x+2 is the Polynomial๛

$\rule{200}{2}$

Answer 2

Answer:

Given:-

→α=2+1√2

→β=2-1√2

To Find:-

→ A Polynomial using Quadratic Formula?

AnsWer:-

•Using Quadratic Formula•

๛k[x²-(α+β)x+αβ]–(1)

→α+β=2+1√2+(2-1√2)

→α+β=4–(2)

→αβ=(2+1√2)×(2-1√2)

→αβ=4-2√2+2√2-2

→αβ=2–(3)

★Using (3)&(2) in (1)★

→k[x²-(4)x+2]

→k[x²-4x+2]

♦Let k=1♦

→1[x²-4x+2]

→x²-4x+2

๛x²-4x+2 is the Polynomial๛

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