Verify that 1,3 and 4 the zeroes of the cubic polynomial p (X) = x3-8x2+19x- 12 and then verify the relationship between the zeroes and the coefficients . And the Following.
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If a & b are zeroes of equations ax² + bx + c = 0 , then equation will be satisfied for value of x .
When, x = 1
p(1) = (1)³ - 8 × (1)² - 19 ×(1) - 12
= p(1) = 1 - 8 - 19 - 12
= p(1) = 1 - 39
= p(1) = -38
When, x = 3
= p(3) = (3)³ - 8 × (3)² - 19 × 3 - 12
= p(3) = 27 - 72 - 57 - 12
= p(3) = 27 - 141
= p(3) = -117
When, x = 4
= p(4) = 4³ - 8 × 4² - 19 × 4 - 12
= p(4) = 254 - 96 - 76 - 12
= p(4) = 254 - 184
= p(x) = 70
This cubic polynomial not satisfied by any value of x .
Therefore, We can say, these zeroes are not this cubic polynomial
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