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secondary 3 | A Maths
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Hi I need help w this ques which requires me to ans using sum and product of roots.
Date Posted: 3 years ago
Views: 159
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3x² - x + 2 = 0
It will be easier to label the roots of this equation as α and β first.
Sum of roots, α+β = -b/a = -(-1)/3 = 1/3
Product of roots, αβ = c/a = 2/3
For the equation to be found, the roots are α² and β²
Sum of roots = α² + β²
= α² + 2αβ + β² - 2αβ
= (α + β)² - 2αβ
= (1/3)² - 2(2/3)
= 1/9 - 4/3
= -11/9
Product of roots = α²β²
= (αβ)²
= (2/3)²
= 4/9
Equation to be found :
x² - (sum)x + product = 0
x² - (-11/9)x + 4/9 = 0
x² + 11/9 x + 4/9 = 0
9x² + 11x + 4 = 0
It will be easier to label the roots of this equation as α and β first.
Sum of roots, α+β = -b/a = -(-1)/3 = 1/3
Product of roots, αβ = c/a = 2/3
For the equation to be found, the roots are α² and β²
Sum of roots = α² + β²
= α² + 2αβ + β² - 2αβ
= (α + β)² - 2αβ
= (1/3)² - 2(2/3)
= 1/9 - 4/3
= -11/9
Product of roots = α²β²
= (αβ)²
= (2/3)²
= 4/9
Equation to be found :
x² - (sum)x + product = 0
x² - (-11/9)x + 4/9 = 0
x² + 11/9 x + 4/9 = 0
9x² + 11x + 4 = 0
Thank you!!
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