(A) Find the sum and product of the roots of the quadratic equation 2 x^2-9 x +4=0.

\[\begin{aligned} & 2 x^{2}-9 x+4=0 \\ & a=2, b=-9, c=4 \end{aligned} \]

Let \(\displaystyle \alpha, \beta\) be roots of \(\displaystyle 2 \mathrm{x}^{2}-9 \mathrm{x}+4=0\)

\[\begin{aligned} & \text { Sum }=\alpha+\beta=-\frac{b}{a}=\frac{9}{2} \\ & \text { Product of roots }=\alpha \beta=\frac{c}{a}=\frac{4}{2}=2 \end{aligned} \]

\[\begin{aligned} & 4 x^{2}-5=0 \\ & a=4, b=0, c=-5 \\ & \text { Discriminant }=b^{2}-4 a c=0-4(4)(-5)=80>0 \\ & \Rightarrow \text { roots are real and distinct. } \end{aligned} \]