Write a quadratic polynomial whose zeroes are
(√2+1) and (√2-1)
Answers
Answer:
Sum of zeroes = √2+1 + √2-1 = 2√2
Product of zeros = (√2+1)(√2-1) = 2-1 = 1
Quadratic polynomial with zeroes (√2+1) and (√2-1) :
x² - (sum of zeroes)x + product of zeros
x² - 2√2x + 1
Answer:
The quadratic polynomial whose zeros are (√2+1) and (√2-1) is given by x²- 2√2x +1
Step-by-step explanation:
To find,
The quadratic polynomial whose zeros are (√2+1) and (√2-1)
Recall the concepts
If the roots are given the quadratic polynomial is given by the expression
x²- (sum of roots)x +Product of roots
Solution:
Given the roots are (√2+1) and (√2-1)
Sum of roots = √2+1 + √2-1 = 2√2
Product of roots = (√2+1) × (√2-1)
= (√2)² - 1² ( by applying the identity (a+b)(a-b) = a² - b² )
= 2 -1
= 1
So we have Sum of roots = 2√2 and product of roots = 1
Hence the quadratic polynomial is x²- 2√2x +1
∴ The quadratic polynomial whose zeros are (√2+1) and (√2-1) is given by x²- 2√2x +1
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