draw a graph fr the polynomial p(x) =x Square _3x_4 and find its zeroes from the graph
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EXPLANATION.
Draw the graph of polynomial p(x) = x² - 3x - 4 = 0.
Finds the zeroes from the graph.
Split into middle term split we get,
⇒ x² - 3x - 4 = 0.
⇒ x² - 4x + x - 4 = 0.
⇒ x ( x - 4 ) + 1 ( x - 4 ) = 0.
⇒ ( x + 1 ) ( x - 4 ) = 0.
⇒ x = -1 and x = 4.
Co-ordinates are = ( -1,0) and (4,0).
Put x = 0 in equation,
⇒ p(x) = y.
⇒ p(0) = y.
⇒ (0)² - 3(0) - 4 = y.
⇒ y = -4.
Their Co-ordinate are = (0,-4).
Put it on Graph it forms parabola upwards.
MORE INFORMATION.
Properties of logarithms.
Let M and N arbitrary positive number such that a > 0, a ≠ 1 , b > 0, b ≠ 1 then,
(1) = ㏒ₐM/N = ㏒ₐM - ㏒ₐN.
(2) = ㏒ₐMN = ㏒ₐM + ㏒ₐN.
(3) = ㏒ₐNᵇ = b㏒ₐN ( b any real number ).
(4) = ㏒ₐᵇNˣ = a/b㏒ₐN (a ≠ 0, b ≠ 0 ).
(5) = ㏒ₐN = ㏒ₙN/㏒ₙᵃ.
(6) = ㏒ₓᵃ. ㏒ₐˣ = 1 = ㏒ₓᵃ = 1/㏒ₐˣ.
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