Question

find the zeores of the polynomial 3x2 - x- 4 and verify the relationship between them


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Answer 1

Step-by-step explanation:

$p(x) = 3x²-x-4$

$let \: p(x) = 0$

$\implies 3x²-x-4 = 0$

$\implies 3x²+3x-4x-4 = 0$

$\implies 3x(x+1)-4(x+1) = 0$

$\implies (x+1)(3x-4) = 0$

$\implies (x+1) = 0 \: \& \: (3x-4) = 0$

$\implies x = -1 \: \& \: x = \frac{4}{3}$

$So, \: the \: zeroes \: of \: p(x) \: are \: -1 \: \& \: \frac{4}{3}$

$Now, \: let \: α = -1 \: \& \: β = \frac{4}{3}$.

$So, \: (α+β) = -1+\frac{4}{3} = \frac{-3+4}{3} = \frac{1}{3}$

$\& \: αβ = (-1)×(\frac{4}{3}) = \frac{-4}{3}$