Question

cube root of nature , product
x²+7x+6=0​

Answer 1

Answer:

as this is a cubic polynomial so we will have three roots of this equation .Lets find one by one

First find the factors of the constant(6) in above equation as:

6=±1,±2,±3,±6

Now using these factors lets see which factor satisfy the given equation as

Put x=1 as

x^3-7x+6=0

(1)^3-7*1+6=0

1-7+6=0

-6+6=0

0=0

So x=1 is the first root of equation.

Now put x=2

(2)^3-7*2+6=0

8-14+6=0

-6+6=0

0=0

So x=2 is another factor.

If we put x=-3

(-3)^3-7*(-3)+6=0

-27+21+6=0

-6+6=0

0=0

I have checked all the factors of constant and these three only satisfy the equation.

Solution set={1,2,-3