Answer:
Length=9 inches,width=4 inches, height =2 inches.
k= [tex]-\frac{111}{8}[/tex]
Step-by-step explanation:
a) If by synethetic division method the remainder equals i.e in the last row and last column if figure yield is 0 then 2 is one of the factor i.e one of the solution of given equation.
Remainder is 0.
Hence 2 is the solution of given equation.
b) Given a box having volume 72 cubic inches
Let Height = x inches
∵ length is 7 inches more than the height
⇒ Length = x+7 inches
& also width is twice the height
⇒ Width = [tex]2\times x[/tex]
Given Volume = 72 cubic inches
[tex]length\times width\times height[/tex] = 72
[tex](x+7)\times (2x)\times x[/tex] - 72 = 0
From part a, 2 is the solution of above equation
⇒ Length = x+7 = 2+7 = 9 inches
Width = [tex]2\times2[/tex] = 4 inches
Height = x = 2 inches
Given [tex]4x-3[/tex] is a factor of [tex]20x^3+23x^{2} -10x+k[/tex]
Hence, [tex]20(\frac{3}{4})^3 +23(\frac{3}{4}) ^{2} -10(\frac{3}{4})+k=0[/tex]
[tex]\frac{135}{16}+\frac{207}{16}-\frac{120}{16} +k=0[/tex]
[tex]\frac{111}{8}+k=0[/tex]
k= [tex]-\frac{111}{8}[/tex]
