Find the zeros of the polynomial x^2+1/6x-2 and verify the relationship between its zeros and coefficients of the polynomial
Answers
Solution :
The polynomial x² + 1/6x - 2.
The zeroes and verify the relationship between it's zeroes and coefficient of the polynomial.
We have p(x) = x² + 1/6x - 2
Zero of the polynomial is p(x) = 0
So;
∴ The α = -3/2 and β = 4/3 are the zeroes of the polynomial.
As the given quadratic polynomial as we compared with ax² + bx + c
- a = 6
- b = 1
- c = -2
So;
Thus;
Relationship between zeroes and coefficient is verified .
Answer:
Step-by-step explanation:
Here the given equation is
x²+(1/6x)-2=0
multiplying the above equation by 6 we get
6x²+x-12=0
or,6x²+9x-8x-12=0
or,3x(2x+3)-4(2x+3)=0
or,(3x-4)(2x+3)=0
Hence the zeros of the polynomial are
x=4/3 andx=-3/2
Now for a quadratic polynomial
ax²+bx+c=0
the relation between coefficient a b and c and their roots m and n are
m+n=-b/a
mn=c/a
For the given equation
m=4/3 n=-3/2
and a=1,b=1/6 and c=-2
now m+n=-1/6
and -b/a=-1/6
therefore,m+n=-b/a
also m x n=-2
and c/a=-2
Hence m x n=c/a