Find the zeroes of a polynomial I am giving down and verify the relationship between the zeroes and the coefficients.
?4s(square)-4s+1
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Question should be:
- Find the zeroes of a polynomial 4s²-4s+1 and verify the relationship between the zeroes and the coefficients.
GIVEN:
- P(s) = 4s²-4s+1
TO FIND:
- Zeros and to verify the relationship between zeros and coefficients.
SOLUTION:
=> 4s²-4s+1 = 0
=> (2s)²-2(2s)(1)+(1)² = 0
=> (2s-1)² = 0
=> (2s-1)(2s-1) = 0
Either (2s-1) = 0
=> 2s = 1
=> s = 1/2
Zeros of P(s) is 1/2 and 1/2
Sum of zeros
= 1/2+1/2
= 2/2
= 1/1
Multiplying numerator and denominator by 4 we get;
= 4/4
=> -(-4)/4 = -(Coefficient of x)/Coefficient of x²
Product of zeros
= (1/2)(1/2)
=> 1/4 = constant term/Coefficient of x²
Verified
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