Question

find the zeros of the following polynomial quadratic polynomial and verify the relationship between the zeros and the coefficient t square minus 15​

Answer 1

Let f(t) be the given polynomial.

f(t)=t^2 -15

Let @ and ß be the zeros of given polynomial.

Of the form,

a^2-b^2=(a+b)(a-b)

Here,

a=t and b=15

f(t)=(t)^2-(√15)^2

=(t+√15)(t-√15)

We know that,

f(t)=0

=>(t+√15)(t-√15)=0

=>t=√15 or t=-√15

=>@=√15 and ß=-√15

Sum of zeros:

@ + ß

=√15+(-√15)

=0

Product of zeros:

@ß=(√15)(-√15)= -15

Hence, verified.