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cupoosta [38]
3 years ago
7

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. (i)1/4 , -1 (ii) √2 ,

1/3​
Mathematics
2 answers:
Viefleur [7K]3 years ago
6 0

Answer:

i) α + β = -1/4, αβ = 1/4

thus p(x) = x² - (α + β)x + αβ = 0

  • x² - (-1/4)x + 1/4 = 0
  • x² + 1/4x + 1/4 = 0
  • 1/4(4x² + x + 1) = 0

ii) α + β = √2, αβ = 1/3

thus p(x) = x² - (α + β)x + αβ = 0

  • x² - (√2)x + 1/3 = 0
  • x² - √2x + 1/3 = 0
  • 1/3(3x² - 3√2x + 1) = 0
My name is Ann [436]3 years ago
3 0

[i] 1/4(4x² + x + 1)

[ii] 1/3(3x² - 3√2x + 1)

<h3>Justification:</h3>

<u>Let α, β be the zeros of polynomial</u>.

[i] We have, α + β = - 1/4 & αβ = 1/4

Thus, polynomial is

<u>p(x) = x² - (α + β)x + αβ</u>

  • x² - (-1/4)x + 1/4
  • x² + 1/4x + 1/4
  • 1/4(4x² + x + 1)

[ii] We have, α + β = √2 & αβ = 1/3

Thus, polynomial is

<u>p(x) = x² - (α + β)x + αβ</u>

  • x² - √2x + 1/3
  • 1/3(3x² - 3√2x + 1)

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