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secondary 3 | A Maths
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help with part (i)
Date Posted: 5 years ago
Views: 199
2x² = 8x + 3
2x² - 8x - 3 = 0
Recall that for the equation ax² + bx + c = 0, sum of roots = -b/a and product of roots = c/a
So,
Sum of roots = α + β = -b/a = -(-8)/2 = 4
Product of roots αβ = c/a = -3/2
For roots 1/β² and 1/α²,
Product = 1/β² x 1/α² = 1/(αβ)²
= 1/(-3/2)²
= 1/(9/4)
= 4/9
Sum = 1/α² + 1/β²
= (β² + α²)/α²β²
= ( (β² + α² + 2αβ) - 2αβ)/(αβ)²
= ( (α+β)² - 2αβ)/(9/4)
= ( 4² - 2(-3/2)) / (9/4)
= (16 + 3) x 4/9
= 19 x 4/9
= 76/9
so equation is :
x² - 76/9 x + 4/9 = 0
9x² - 76x + 4 = 0
2x² - 8x - 3 = 0
Recall that for the equation ax² + bx + c = 0, sum of roots = -b/a and product of roots = c/a
So,
Sum of roots = α + β = -b/a = -(-8)/2 = 4
Product of roots αβ = c/a = -3/2
For roots 1/β² and 1/α²,
Product = 1/β² x 1/α² = 1/(αβ)²
= 1/(-3/2)²
= 1/(9/4)
= 4/9
Sum = 1/α² + 1/β²
= (β² + α²)/α²β²
= ( (β² + α² + 2αβ) - 2αβ)/(αβ)²
= ( (α+β)² - 2αβ)/(9/4)
= ( 4² - 2(-3/2)) / (9/4)
= (16 + 3) x 4/9
= 19 x 4/9
= 76/9
so equation is :
x² - 76/9 x + 4/9 = 0
9x² - 76x + 4 = 0
See 1 Answer
done
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clear
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part i
Date Posted:
5 years ago
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