F4 MATHS 3題

先生

2010-10-17 7:18 pm

If α is not equal to β and
{2α^2-hα-b=0
{2β^2-hβ-b=0
Find 1/α+1/β in terms of h and b
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Form an quadratic equation with integral coefficients if one root is equal to 5+√2
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If f(x) = x^2+2 and g(x) = 2x+1, find f(g(x))
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回答 (1)

用戶2053

2010-10-17 7:46 pm

✔ 最佳答案

1)α , β are the roots of 2x² - hx - b = 0α + β = h/2
α β = - b/21/α + 1/β= (α + β) / (α β)= (h/2) / (-b/2)= - h / b
2)Set the other root = 5 - √2 ,The required equation is :x² - (5 + √2 + 5 - √2)x + (5 + √2)(5 - √2) = 0i.e.x² - 10x + (5² - 2) = 0i.e.x² - 10x + 23 = 0
3) f ( g(x) )= f (2x+1)= (2x+1)² + 2= 4x² + 4x + 3

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