Question

Find the zeroes of the polynomial x^2+1/6x-2 and verify the realtion between the coefficient and zeroes of the polynomial.​

Answer 1

Answer:

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

Hence the relation between the coefficients of polynomial and its roots (or zeros) are verified.

mark me as brainlist...

Answer 2

Answer:

Let f(x) = x2 + 1/6x - 2

Here a = 1, b = 1/6 and c = -2

x2 + 1/6x - 2 = 0

Multiplying by 6 throughout, we have

6x2 + x - 12 = 0

6x2 + 9x - 8x - 12 = 0

3x(2x + 3) - 4(2x + 3) = 0

(2x + 3)(3x - 4) = 0

2x + 3 = 0 or 3x - 4 = 0

x = -3/2 or x = 4/3

Sum of roots = -3/2 + 4/3 = -1/6

-b/a = -1/6/1 = -1/6

So, Sum of roots = -b/a

Product of roots = -3/2*4/3 = -2

c/a = -2/1 = -2

So, Product of roots = c/a