Question

find all the zeros of y cube minus 19 Y + 30 if it is given that one of its zeros is 2​

Answer 1

y³-19y+30 is p(x)

x-2 is g(x)

On dividing it we get, y²+2y-15

= y² -3y +5y -15

=y(y-3) +5(y-3)

=y+5 or y-3

=y=-5 or 3

So the zeroes of polynomial are 2,3 and -5

Answer 2

here, 2 is one of the zero of p(y)

then , (y - 2) is a factor of p(y)

so we divide (y^3 -19y+30) by (y - 2) , we get :-

y^2 - 2y -15 as a quotient.

then , factories the quotient , we get :-

(y - 5) (y + 3) as a result....

then , y - 5 = 0

y = 5

& y + 3 = 0

y = - 3

hence , the remaining two zeros are : 5 & - 3 .