Question

Factor completely 3x2 + x + 7.

Answer 1

Answer:

Option 3 - The given equation is a prime.

Step-by-step explanation:

Given : Quadratic equation $3x^2+x+7=0$

To find : The factors of given equation.

Solution : To factories the given equation $3x^2+x+7=0$

We will apply discriminant method

General form - $ax^2+bx+c=0$

$D=b^2-4ac$

Solution is $x=\frac{-b\pm\sqrt{D}}{2a}$

Equation is $3x^2+x+7=0$

where a=3 , b=1, c=7

$D=b^2-4ac$

$D=(1)^2-4(3)(7)$

$D=1-84$

$D=-83$

Solution is $x=\frac{-b\pm\sqrt{D}}{2a}$

$x=\frac{-1\pm\sqrt{-83}}{2(3)}$

$x=\frac{-1\pm\sqrt{83}i}{6}$

$x=\frac{-1+\sqrt{83}i}{6},\frac{-1-\sqrt{83}i}{6}$

Therefore, The factors are

$[x+(\frac{-1+\sqrt{83}i}{6})][x-(\frac{-1-\sqrt{83}i}{6})]$

So, 1,2,4 are not the options.

Now, check for prime

In a quadratic equation if $D=\sqrt{b^2-4ac}$ form a complete square then it is not prime and vice-versa.

In this question $D=\sqrt{-83}$  does not make a perfect square.

Therefore, It is a prime.

Option 3 is correct.

Answer 2

It should be prime :DDD