Question

Q-1) If both (x-2) and (x-1/2) are factors of Px^2+5x+r,show
that p=r.
Q-2) If x and y are two positive real numbers such that 9x^2+4y=97 and xy=6,then find them value of 27x^3+8y^3.

Answer 1

x-2=0
x=2
px^2+5x+r=0
p(2)^2+5(2)+r=0
4p+10+r=0
4p+r=-10
p+r=-10/4
p+r=-5/2