Find all the zeros of the polynomial function p(x) = 2x4 + x3 − 19x2 − 9x + 9. Enter them from least to greatest.
Answers
Answer:
x = -3, 1/2 , 3, -1.
Increasing function of zeroes of given function is -3 < -1 < 1/2 < 3
Step-by-step explanation:
p(x) = 2x⁴+ x³- 19x²- 9x+9
This is biquadratic polynomial because it has a degree 4. So there is not any particular way to find it's zeroes. You have follow hit and trial method to find the zeroes.
At x = -1 , p(x) = 0 ( Put -1 at place of x you will get zero. It means (x+1) is a factor of this polynomial. Devide this polynomial by (x+1) you will get a cubic polynomial 2x³- x³- 18x+ 9. Apply hit and trial on this cubic polynomial also.
At x = 3, cubic polynomial become zero. It means (x-3) is also a factor of p(x). Divide the cubic polynomial by (x-3) you get a quadratic polynomial 2x²+ 5x- 3. Factorise this quadratic polynomial. You will get other two factors (x+3) and (2x-1).
So, the final answer is zeros of p(x) is -3, 1/2, 3 and -1.