# University Maths Solution

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Maths Question
Question 1

If the two roots of the equation ${{x}^{4}}+a{{x}^{3}}+b{{x}^{2}}+cx+d=0$ are such that one is the negative of the other, show that ${{c}^{2}}=a(bc-ad)$

Question 2

$\text{Show that the polynomial }{{x}^{4}}+4{{x}^{3}}+6{{x}^{2}}-8\text{ is divisible by }x+2$

Question 3

$\text{By using the remainder theorem, factorise completely }{{x}^{4}}-10{{x}^{3}}+35{{x}^{2}}-50x+24$

Question 4

\begin{align} & \text{Given that }x-1\text{ and }x-2\text{ are factors of the polynomial }{{x}^{3}}+a{{x}^{2}}+bx-6.\text{ } \\ & \text{Find }a\text{ and }b \\\end{align}

Question 5

$\text{Find the remainder when }{{x}^{4}}-3{{x}^{3}}+4{{x}^{2}}-6x+7\text{ is divided by }x-1$

Question 6

\begin{align} & \text{Use the remainder theorem to factorise completely the expression}\, \\ & {{x}^{3}}(y-z)+{{y}^{3}}(z-x)+{{z}^{3}}(x-y) \\\end{align}

Question 7

$\text{Solve the equation by using Remainder theorem }{{x}^{4}}-16{{x}^{3}}+80{{x}^{2}}-176x+105=0$

Question 8

\begin{align} & \text{Solve the following equation by using Remainder theorem} \\ & \text{ }{{x}^{3}}-15{{x}^{2}}+74x-120=0 \\\end{align}

Question 9

\begin{align} & \text{Solve the following equation by using Remainder theorem} \\ & {{x}^{3}}-(5+a){{x}^{2}}+(6+5a)x-6a=0 \\\end{align}