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Answered by
2
Answer:
x² - 6x + 11 = 0,
Step-by-step explanation:
Hi,
Let α, β be the roots of the equation
x² - 2x + 3 = 0,
Let f(x) = x² - 2x + 3
Given that roots are increased by 2, so new roots
of the equation are α + 2, β + 2
Let y = α + 2 which is the required root of new
equation,
So, α = y - 2
But, we know α is root of f(x), hence
f(α) = 0
But α = y - 2, so
f(y - 2) = 0
(y - 2)² - 2(y - 2) + 3 = 0
y² - 6y + 11 = 0,
Since similar argument hold for other root as
well, hence this equation represents the one
with roots α + 2 and β + 2
Changing the variable y to x, we get
x² - 6x + 11 = 0, which is the required equation.
Hope, it helps !
Answered by
4
Answer:
x²- 2x + 3 = 0
a+b = -b/a = -(-2)/1= 2
a(b) = c/a = 3/1 = 3
alpa³+ beta³= (a+b)³- 3ab(a+ b)
= (2)³- 3(3) (2)
= 8 - 9(2)
= 8 - 18
= -10
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