Find all the roots of each of the polynomial equations. \( \begin{array}{ll}\text { 9. } x^{3}-2 x^{2}-11 x-6=0 & \text { 10. } x^{3}-11 x^{2}+36 x-26=0 \\ \text { 11. } 2 x^{3}+x^{2}+4 x-15=0 & \text { 12. } x^{3}-5 x^{2}+39 x+45=0 \\ \text { 13. } 2 x^{3}+x^{2}-108 x-54=0 & \text { 14. } x^{3}+2 x^{2}-23 x+6=0 \\ \text { 15. } x^{3}+10 x^{2}+13 x-74=0 & \text { 16. } x^{4}+5 x^{3}+23 x^{2}+51 x=0\end{array} \)

D) A student claimed that the largest integer of \( k \) for which the graph \( y=2 x^{2}-3 x+k-1 \) meets the \( x \)-axis is 2 . Verify this statement.

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

\( \begin{array}{ll} & \text { Solve for } x: \\ 2.1 & (x-5)(x+3)=0 \\ 2.2 & 2^{x-1}=10-2^{x+1} \\ 2.3 & 5^{3 x-6}=125 \\ 2.4 & \frac{x^{2}-3}{2}=x\end{array} \)

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 : \( \begin{array}{lll}\text { (iv) } x^{2}-2 x-8 & \text { (ii) } 4 s^{2}-4 s+1 & \text { (iii) } 6 x^{2}-3-7 x \\ \text { (iv) } 4 u^{2}+8 u & \text { (v) } s^{2}-15 & \text { (vi) } 3 x^{2}-x-4\end{array} \)