Find a polynomial whose zeroes are √2 and -√2.
Answers
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:
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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