For some real number $r,$ the polynomial $8x^3 - 4x^2 - 42x + 45$ is divisible by $(x - r)^2.$ Find $r.$
My go at it:
I immediately tried factoring it, and magically, the factored expression was:
$(2x-3)^2(2x+5)$, obviously we want (x-r)^2 to be divisible so I though 3x+3 would divide the $(2x-3)^2$,
however the question is asking for a real number $r$, then is there a number $r3?,
Remember, vietas formula for three roots is for x, y, z are roots,
x+y+z=-b/a
xy+yz+xz=c/a
xyz=-d/a
for a cubic polynomial ax^3+bx^2+cx+d
