Find all rational zeros of the polynomial, and write the polynomial in factored form. P(x)=4x^{3}-7x+3

defazajx 2021-05-09 Answered
Find all rational zeros of the polynomial, and write the polynomial in factored form.
P(x)=4x37x+3
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

insonsipthinye
Answered 2021-05-11 Author has 83 answers
Step 1
Given:
P(x)=4x37x+3
First check the solution of cubic equation by putting the different value of x.
If x=1
P(1)=4(1)37(1)+3=77=0
So, x = 1 is the solution of given cubic equation.
4x37x+3 is divided by x-1
4x37x+3x1=4x2+4x3
Step 2
Factorize 4x2+4x3
4x22x+6x3=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=12 or x=32
So,
Zeroes of polynomial are: x=1, x=12,x=32
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more