Find the roots of the equation x² + 7x + 10 = 0

We will use the concept of factorization of a polynomial to find the roots of the equation.

Answer:The roots of the equation x² + 7x + 10 = 0, is -5 and -2.

Let's see how we will use the concept of factorization of a polynomial to find the roots of the equation.

Explanation :

For the equation x² + 7x + 10 = 0

The above equation can also be written in the form of x² + 5x + 2x + 10 = 0 [ splitting the middle term ]

Now factorizing x from the first term of the expression i.e. ( x² + 5x ) and factorizing 2 from the second term of the expression i.e. 2x + 10.

After factorizing the resulting equation we get  x ( x + 5 ) + 2 ( x + 5 ) = 0

Now using distributive property we get  ( x + 2 ) ( x + 5 ) = 0

On equating both the terms separately with 0 we get,

Hence, roots of the equation x² + 7x + 10 = 0 are -5 , -2.