"Find all rational zeros of the polynomial, and..." was answered by our community

defazajx

Answered question

2021-05-09

Find all rational zeros of the polynomial, and write the polynomial in factored form.

P (x) = 4 x^{3} - 7 x + 3

insonsipthinye

Skilled2021-05-11Added 83 answers

Step 1
Given:

P (x) = 4 x^{3} - 7 x + 3

First check the solution of cubic equation by putting the different value of x.
If x=1

P (1) = 4 {(1)}^{3} - 7 (1) + 3 = 7 - 7 = 0

So, x = 1 is the solution of given cubic equation.

4 x^{3} - 7 x + 3

is divided by x-1

\frac{4 x^{3} - 7 x + 3}{x - 1} = 4 x^{2} + 4 x - 3

Step 2
Factorize

4 x^{2} + 4 x - 3

4 x^{2} - 2 x + 6 x - 3 = 0

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

x = \frac{1}{2}

x = - \frac{3}{2}

So,
Zeroes of polynomial are: x=1,

x = \frac{1}{2}, x = - \frac{3}{2}

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