We have an answer to "Find all the zeros for: y=x3−2x2−5x+6"

Barbara Schroder

Answered question

2021-11-17

Find all the zeros for:

y = x^{3} - 2 x^{2} - 5 x + 6

Symbee

Beginner2021-11-18Added 17 answers

Step 1
Given that,

y = x^{3} - 2 x^{2} - 5 x + 6

and we have to calculate the zeros of the function.
We know that,
for zeros of the function we find the fractions of the function.
Step 2
If we put

x = - 2

in given function then the value of function is zero,
thus we can say that,

(x + 2)

is a fraction of given function.
And when we divide the function by

(x - 2)

then, quotient will be

(x^{2} - 4 x + 3)

.
thus we can write the given function as,

(x - 2) (x^{2} - 4 x + 3) = 0

(x - 2) (x^{2} - 3 x - x + 3) = 0

(x - 2) [x (x - 3) - (x - 3)] = 0

(x - 2) (x - 3) (x - 1) = 0

x = 1, 2, 3

Answer: Thus zeros of the given function are (1, 2, 3).

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