Question

A) Use synthetic division to show that 2 is a solution of 2h3 +14h2 − 72 = 0 .

Answer 1

Answer:

Length=9 inches,width=4 inches, height =2 inches.

k= $-\frac{111}{8}$

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 = $2\times x$

   Given   Volume = 72 cubic inches

   $length\times width\times height$ = 72

   $(x+7)\times (2x)\times x$ - 72 = 0

From part a, 2 is the solution of above equation

⇒       Length = x+7 = 2+7 = 9 inches

          Width = $2\times2$ = 4 inches

         Height = x = 2 inches

Given $4x-3$ is a factor of $20x^3+23x^{2} -10x+k$

Hence, $20(\frac{3}{4})^3 +23(\frac{3}{4}) ^{2} -10(\frac{3}{4})+k=0$

            $\frac{135}{16}+\frac{207}{16}-\frac{120}{16} +k=0$

                   $\frac{111}{8}+k=0$

                      k= $-\frac{111}{8}$