Question

EXAMPLE 6 Find the zeros of the polynomial x+1/6x-2, and verify the relation between the
coefficients and zeros of the polynomial.
[NCERT EXEMPLAR]

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.

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