Question

find the roots of equation x³-3x²+4x-2=0​

Answer 1

Answer:

Zeroes of f(x) are those values of f(x) for which, f(x)= 0

f(x)= x^3 - 3x^2 -4x +12=0

Solution of this cubic function, will be the zeroes…

so for solving above , we factorize it first. It has 3 linear factors, as its degree is 3.

x^3- 3x² -4x +12 =0

=> x²(x-3) -4(x-3) =0

=> (x-3)(x²-4) =0

=> (x-3) ( x+2) (x-2) =0

If product of 3 factors is zero, either of them will be 0,

If (x-3)=0 , then, x=3…………(1)

If (x+2) = 0 then, x= -2………….(2)

If (x-2) =0 then x= 2……………..(3)

So zeroes are 3,2 & -2

For all these values, f(x)=0

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