Question

Write a quadratic polynomial whose zeroes are 2 + √2 and 2-√2​

Answer 1

Answer:

Let the zeroes of the quadratic polynomial be α=

2

,β=2

2

Then, α+β=

2

+2

2

=

2

(1+2)=3

2

αβ=

2

×2

2

=4

Sum of zeroes =α+β=3

2

Product of zeroes =αβ=4

Then, the quadratic polynomial =x

2

−( sum of zeroes )x+ product of zeroes =x

2

−(3

2

)x+4

=x

2

−3

2

x+4

Step-by-step explanation:

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Answer 2

Answer:

$\alpha = 2 + \sqrt{2} \\ \beta = 2 - \sqrt{2}$

Substitute in

$x {}^{2} + x( \alpha + \beta ) + ( \alpha \beta )$

$\alpha + \beta = 2 + \sqrt{2} + 2 - \sqrt{2} = 4$

$\alpha \beta = (2 + \sqrt{2} )(2 - \sqrt{2)} = 4 - 2 \sqrt{2} + 2 \sqrt{2} - 2$

$= > 2$

therefore eqn will be

x²+4x+2

Step-by-step explanation:

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