Question Two

$(a)$ Determine the nature $of$ the roots for the equation $x^2+2x-15=0.$ Hence $if$ possible solve the

equation

$(b)$ The roots $of$ the equation $x^2+kx-7=0$ are $and-1.$ Find the value $ofk.$

$(c)$ Complete the square $inf(x)=-2x^2+4x+8$ and sketch the curve $off(x)$

$(d)$ Find the value $ofkin$ each $of$ the following $if$:

$(i)$ The roots $of3x^2-5x+k=0$ differ $by2.$

$(ii)$ The roots $of3x^2+(k-1)x-2=0$ are equal and opposite.

Question Three

$aV(t)=-2t^2+8t+3,$ where $tis$ time $in$

seconds.

$iV(t)$

iiP$(R)=R^2-6R+13,$ where $Ris$ resistance $in$ ohms.

$iP(R)$

iiR that minimizes power dissipation.

iiiV$(t)=a{t}^2+bt+c,$ and

measurements give $V(1)=5v,V(2)=8v$ and $V(3)=13v.$ Determine the quadratic function

$V(t)$ and compute the time when the voltage $isat$ a minimum $or$ maximum.

$dV(Z)=Z^2-8Z+16.$ Find

the impedance $Z$ that results $in$ the minimum voltage drop, and determine the minimum value.

$eQ(t)=-t^2+6t,$ where $Qis$ the charge $at$ time $t$ hours.

$iQ(t)$

$ii$