Option (2): x³ + x² + 7x - 2 = 0
Step-by-step explanation:
The given equation is as:
x³ - x² + 7x + 2 = 0
Here, for your kind information I'm using alpha, beta, gamma as a, b, and c respectively! Right
(i) Sum of roots = (-a) + (-b) + (-c)
= -(a + b + c)
= - (- Coefficient of x²/ Leading coefficient )
= - 1
(ii) Sum of product of roots taken two at a time =
a.b + b.c + a.c = Coefficient of x/ Leading coefficient
= 7
(iii) Product of roots = - a.b.c
= - (- Constant term/ Leading coefficient)
= 2
Required equation having -a, - b, - c as roots can be written as
x³ - (a + b + c)x² + (a.b + b.c + c.a)x - abc = 0
=> x³ - (-1) x² + 7x - 2 = 0
=> x³ + x² + 7x - 2 = 0
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