Question

Find a polynomial whose zeroes are √2 and -√2.​

Answer 1

Given alpha=root2 beta=-root2

Sum of zeroes(alpha+beta)=root2-root2=0

Product of zeroes(alpha×beta) =root2×-root2=-2

Quadratic polynomial formula

K[x^2-(alpha+beta)x+(alpha×beta)]

K[x^2-0x-2]

K[x^2-0-2]

K[x^2-2]

K=1

1[x^2-2]

x^2-2 is the required quadratic polynomial

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Answer 2

Answer:

The polynomial whose zeroes are √2 and -√2 is given by x² -2

Step-by-step explanation:

Given,

The zeros of the polynomial are √2 and -√2.​

To find,

The equation of the polynomial

Recall the formula

If α and β  are the roots of the polynomial, then the polynomial is given by the formula

x² - (α+β)x+ αβ

Solution:

Since the zeros of the polynomial are √2 and -√2, we have

α = √2 and β = -√2

Then α + β = √2+-√2 = 0

αβ = √2×-√2 = -2

Hence, the required polynomial = x² - (α+β)+ αβ

= x² - 0x -2

= x² -2

∴ The polynomial whose zeroes are √2 and -√2 is given by x² -2

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