Find the zeroes of the quadratic polynomial f(x)=6x²-3 and verify the relationship between the zeroes and its coefficients.
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f(x) = 6x²-3
f(x) = 0
6x²-3 = 0
6x² = 3
x² = 3/6
x² = 1/2
x = 1/√2 , -1/√2
Roots of f(x) = 1/√2 , -1/√2
Verification = (i) 6(1/√2)² - 3
= 6(1/2) - 3
= 3-3
= 0
(ii) 6(-1/√2)² - 3
= 6(1/2) - 3
= 3-3
= 0
f(x) = 0
6x²-3 = 0
6x² = 3
x² = 3/6
x² = 1/2
x = 1/√2 , -1/√2
Roots of f(x) = 1/√2 , -1/√2
Verification = (i) 6(1/√2)² - 3
= 6(1/2) - 3
= 3-3
= 0
(ii) 6(-1/√2)² - 3
= 6(1/2) - 3
= 3-3
= 0
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