\( b \) are constants. (i) Find the value of \( a \) and of \( b \). (ii) Hence solve the equation \( \mathrm{f}(x)=0 \). \( \mathrm{f}(x)=2 x^{3}+a x^{2}-7 a^{2} x-6 a^{3} \), where \( a \) is a constant. (i) Show that \( x+a \) is a factor of \( \mathrm{f}(x) \). (ii) Hence find the real roots of the equation \( \mathrm{f}(x)=0 \). 18. Given that \( x^{2}+2 x-3 \) is a factor of \( \mathrm{f}(x) \), where \( \mathrm{f}(x)=x^{4}+6 x^{3}+2 a x^{2}+b x-3 a \)

Given that the quadratic equation \( p x^{2}-9 q x+9 p=0 \), where \( p \) and \( q \) are constants, has two equal roots. Find \( p: q \). [2 marks.

(c) Subtract: \( 31(1-4 m+5 n) \) from \( 4 I(10 n-3 m+21) \) (d) Subtract: \( 3 a(a+b+c)-2 b(a-b+c) \) from \( 4 c(-a+b+c \)

19 days of March 2015 . \( \begin{array}{llll}\text { (1) } ₹ 1530 & \text { (2) } ₹ 1260 & \text { (3) } ₹ 1620 & \text { (4) } ₹ 1710\end{array} \) \( x \propto \frac{1}{y} \). When \( y=6, x=14 \). What is the constant of variation ? \( \begin{array}{llll}\text { (1) } 94 & \text { (2) } 84 & \text { (3) } 82 & \text { (4) } 72\end{array} \) If \( x \) varies directly as \( y \), which number will replace the question

\( \frac { 1 } { r } \times \frac { 1 - ( \frac { 1 } { r } ) ^ { n } } { 1 - \frac { 1 } { r } } \geq \frac { 9 r } { 100 } \Rightarrow 1 - \frac { 1 } { r ^ { n } } \geq \frac { 9 r } { 100 } \)

Simplify the expression: \( (x^{1/4}y^{1/2})^{8} \)