Find the value of k, if 2x - 3 is a factor of 2x³ + kx² + x + 12
URGENT!!!!
AvmnuSng:
do you know division of two polynomials ??
No
Answers
Answered by
12
By using factor theorem,
If 2x - 3 is 0, then x = 3/2
Now substitute the value of x in the equation
2x^3+kx^2+x + 12 = 0
2 (3/2)^3 + k (3/2)^2 + 3/2 + 12 = 0
54/8 + k(9/4) + 27/2 = 0
81/4 + k(9/4) = 0
k = -81/4
9/4
= 9
If 2x - 3 is 0, then x = 3/2
Now substitute the value of x in the equation
2x^3+kx^2+x + 12 = 0
2 (3/2)^3 + k (3/2)^2 + 3/2 + 12 = 0
54/8 + k(9/4) + 27/2 = 0
81/4 + k(9/4) = 0
k = -81/4
9/4
= 9
it's -9 not 9, make correction to your solution
Answered by
7
2x-3 is a factor of 2x^3+kx^2+x+12
2x-3=0
2x-3+3=0+3
2x=3
x=3/2
x=1.5
substituting x=1.5 in 2x^3+kx^2+x+12
2(1.5)^3+k(1.5)^2+1.5+12=0
2(3.375)+k(2.25)+13.5=0
2.25k+6.75+12+1.5=0
2.25k+20.25=0
2.25k=-20.25
k=-9
2x-3=0
2x-3+3=0+3
2x=3
x=3/2
x=1.5
substituting x=1.5 in 2x^3+kx^2+x+12
2(1.5)^3+k(1.5)^2+1.5+12=0
2(3.375)+k(2.25)+13.5=0
2.25k+6.75+12+1.5=0
2.25k+20.25=0
2.25k=-20.25
k=-9
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