Question

find zeroes 6x^2-3 and verify the relationship between zeroes and coefficient​

Answer 1

Let @ and ß be the zeros of the polynomial.

Consider the polynomial to be f(x).

f(x)=6x²-3

=(√6x√33)(√6x-√3)

Now,

f(p)=0

→(√6x+3)(√6x-√3)=0

→√6x-√3=0 or √6x+√3=0

→x=√3/√6 or - √3/√6

→x= 1/√2 or -1/√2

→@=1/√2 and ß= -1/√2

Verification:

•Sum of zeros:

@+ß

=1/√2 -1/√2

=0

•Product of zeros:

@ß

=1/√2(-1/√2)

= -1/2

Hence,verified

•Some rules of polynomials:

Sum of zeros: - x coefficient/x²coefficient

Product of zeros: constant term/x²coefficient