Question

EXERCISE 2.2
nd the zeroes of the following quadratic polynomials and verify the relatio
e zeroes and the coefficients.
4s2subtrect4sadd1​

Answer 1

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Answer 2

Let p(s) represent the given polynomial

We have,

p(s)=4s²-4s-1

Let @ and ß be the zeros of the above polynomial

Now,

p(s)=4s²-4s-1

=4s²-2s-2s-1

=2s(2s-1)-1(2s-1)

=(2s-1)(2s-1)

By factor theorm,

p(s)=0

→(2s-1)(2s-1)=0

→(2s-1)=0 or (2s-1)=0

→s=1/2 or s=1/2

→@=1/2 and ß=1/2

★Verification:

•Sum of zeros:

@+ß

=1/2+1/2

=2/2

=1

•Product of zeros:

@ß

=1/2×1/2

=1/4