18 Consider the equation \( x^{2}-2 x+r=0 \), where \( r \) is a real parameter. \( 1^{\circ} \) Calculate \( r \) so that the roots \( x_{1} \) and \( x_{2} \) exist. \( 2^{\circ} \) Calculate \( r \) so that : \( \begin{array}{lll}\text { a) } \frac{1}{x_{1}}+\frac{1}{x_{2}}=-\frac{1}{2} & \text {; b) } x_{1}^{2}+x_{2}^{2}=6 & \text {; ce } \frac{1}{x_{1}^{2}}+\frac{1}{x_{2}^{2}}=1 \\ \text { d) }\left(x_{1}-x_{2}\right)^{2}=4 & \text {; e) } \frac{1}{x_{1}-2}+\frac{1}{x_{2}-2}=3\end{array} \)

3.1.2 The number pattern is quadratic and \( T_{4}=2+5 y \). 3.2 In a linear number pattern, the \( 19^{\text {th }} \) term is 40 and the \( 7^{\text {th }} \) term is 16 . Thus, determine the first two terms.

18. \( \begin{aligned} y & =x-5 \\ y & =-2 x-5\end{aligned} \)

\( 22 \quad \frac { 1 } { 4 } x - \frac { 5 } { 2 } = - 2 \)

Find the slope and the \( y \)-intercept of the graph of the equation. \[ 8 x+9 y=36 \] slope \( y \)-intercept \( \quad(x, y)=(\square) \)

प्रश्नाबानी 2.2 निम्न द्विघात बहुपदों के शून्यक ज्ञात कीजिए और शून्यकों तथा गुणांकों के बीच के संबंध की सत्यता की जाँच कीजिए : \( \begin{array}{lll}\text { (iv) } x^{2}-2 x-8 & \text { (ii) } 4 s^{2}-4 s+1 & \text { (iii) } 6 x^{2}-3-7 x \\ \text { (iv) } 4 u^{2}+8 u & \text { (v) } s^{2}-15 & \text { (vi) } 3 x^{2}-x-4\end{array} \)