Question

the polynomial x cube + 2 X + 3 has how many roots​

Answer 1

Answer:

There are 3 roots of this polynomial because it's highest power is 3.

hope it will help you!..

Answer 2

Answer:

Number of roots of given polynomial are 3.

Step-by-step explanation:

Here given polynomial is ${x}^{3} + 2x + 3$

Let,$f(x) = {x}^{3} + 2x + 3$

Here we want to find root of the polynomial f(x).

Now,$f(x) = 0$

${x}^{3} + 2x + 3 = 0$

${x}^{3} + {x}^{2} - {x}^{2} - x + 3x + 3 = 0$

${x}^{2} (x + 1) - x(x + 1) + 3(x + 1) = 0$

$(x + 1)( {x}^{2} - x + 3) = 0$

If product of two term is zero then they are separately zero.

So,$(x + 1) = 0$and ${x}^{2} - x + 3 = 0$

Now,

$x + 1 = 0 \\ x = - 1$

and

${x}^{2} - x + 3 = 0 \\x = \frac{ - ( - 1)\pm( {( - 1)}^{2} - 4 \times 3 \times 1 }{2 \times 1} \\ x = \frac{ 1+ \sqrt{-11} }{2} \: or \: \frac{ 1-\sqrt{-11} }{2}$

(By Sridhar Acharya theorem)

Roots of equation f(x)=0 are -1,

$\frac{ 1+ \sqrt{-11} }{2}$

and $\frac{ 1 - \sqrt{-11} }{2}$

So, number of roots of given polynomial are 3.