mat 2001 Q2

mat · Uk 15 marks Factor & Remainder Theorem Factorization and Root Analysis
(a) Factorize the expression $x ^ { 2 } + 3 x - 10$.
(b) If $x ^ { 3 } + a x ^ { 2 } + b x + c = ( x - \alpha ) ( x - \beta ) ( x - \gamma )$ for all values of $x$, find $a , b , c$ in terms of $\alpha , \beta , \gamma$.
(c) Find a value of $b$ for which $x ^ { 3 } + b x + 2 = 0$ has exactly two distinct solutions.
\frac { 1 } { 5 }$ the gradient will attain its maximum either at an endpoint ( 0 or $2 \frac { 1 } { 5 }$ ), or at a maximum turning point. Note 
(a) Factorize the expression $x ^ { 2 } + 3 x - 10$.

(b) If $x ^ { 3 } + a x ^ { 2 } + b x + c = ( x - \alpha ) ( x - \beta ) ( x - \gamma )$ for all values of $x$, find $a , b , c$ in terms of $\alpha , \beta , \gamma$.

(c) Find a value of $b$ for which $x ^ { 3 } + b x + 2 = 0$ has exactly two distinct solutions.
Paper Questions
Q1 Q2 Q3 Q4 Q5