Question

obTain all the zeroes of the polynomial x4-17x2-36x-20 if two of it's zeroes are 5 and -2

Answer 1

Let the zeros be a,b,c and d

Then,

$S_1=a+b+c+d=0$

$\implies\;a+b+5+(-2)=0$

$\implies\bf\;a+b=-3$..........(1)

$S_4=abcd=-20$

$\implies\;ab(5(-2))=-20$

$\implies\bf\;ab=2$..........(2)

Using (1) and (2), we get

$a(-3-a)=2$

$-3a-a^2-2=0$

$a^2+3a+2=0$

$(a+1)(a+2)=0$

$\implies\;a=-1,-2$

when a=-1, b=-2

when a=-2, b=-1

$\therefore\textsf{The zeros of the given polynomial are }\;-1,\;-2,\;5,\;-2$