If x= -1/3 is a zero of a polynomial . p( x)= 27 x³ -ax² -x+3, then find the value of a.
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27 x -1/27-a x 1/9+1/3+3=0
-1-a x 1+3/9+3=0
-1-4/9=-3
a=-2 x 9/-4=9/2
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Hey there !
x = -1/3
p [ - 1/3 ] = 27 × [ -1/3 ]³ - a × [ -1/3 ]² - [ -1/3 ] + 3
-27 - 1/6a + 1/3 + 3 = 0
-24 - 1/6a + 1/3 = 0
- 1/6a + 1/3 = 24
-1/6a = 24 - 1/3
-1/6a = 24 x 3 / 3 - 1/3
-1/6a = 72/3 - 1/3
-1/6a = 71/3
a = 71/3 x -6/1
a = -142
x = -1/3
p [ - 1/3 ] = 27 × [ -1/3 ]³ - a × [ -1/3 ]² - [ -1/3 ] + 3
-27 - 1/6a + 1/3 + 3 = 0
-24 - 1/6a + 1/3 = 0
- 1/6a + 1/3 = 24
-1/6a = 24 - 1/3
-1/6a = 24 x 3 / 3 - 1/3
-1/6a = 72/3 - 1/3
-1/6a = 71/3
a = 71/3 x -6/1
a = -142
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