Find the zeroes of the quadratic polynomial t2 -9 and verify the relationship
between the coefficients and its zeroes.
Answers
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Answer:
Zeros are 3 & -3
Explanation:
Given polynomial,
⇒ t² - 9
Or, it can be written as,
⇒ (t)² - (3)²
Using the identity :- a² - b² = (a + b)(a - b)
We can say that,
⇒ (t)² - (3)² = (t + 3)(t - 3)
Then, zeros of the polynomial are
⇒ t = 3, -3
Verification of the relationship between the coefficient and it's zeros,
Sum of zeros,
- α + β = 3 + (-3) = 0
Product of zeros,
- αβ = (3)(-3) = -9
Hence, verified !
_____________________
General form of a quadratic equation :-
- ax² + bx + c
Identity used :-
- (a + b)(a - b) = a² - b²
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