Question

How do you solve \[{x^2} + 3x + 2 = 0\] using quadratic formula?

Answer 1

Hint: Here we are given with a quadratic equation. To solve the quadratic equation is nothing but finding the factors of the equation. Using a quadratic formula is finding the roots with the help of discriminant. We will compare the given quadratic equation with the general quadratic equation of the form \[a{x^2} + bx + c = 0\] . So let’s start solving!
Formula used:
Quadratic formula: \[ \Rightarrow \dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}\]

Complete step-by-step answer:
Given the equation \[{x^2} + 3x + 2 = 0\]
Comparing it with standard quadratic equation \[a{x^2} + bx + c = 0\] we get \[a = 1,b = 3\& c = 2\]
Now we will use the quadratic formula mentioned above to find the factors.
 \[ \Rightarrow \dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}\]
Substituting the values,
 \[ = \dfrac{{ - 3 \pm \sqrt {{3^2} - 4 \times 1 \times 2} }}{{2 \times 1}}\]
Solving the root,
 \[ = \dfrac{{ - 3 \pm \sqrt {9 - 8} }}{2}\]
 \[ = \dfrac{{ - 3 \pm \sqrt 1 }}{2}\]
We know that the root of 1 is 1.
 \[ = \dfrac{{ - 3 \pm 1}}{2}\]
Now we will get two different values of the root.
 \[ = \dfrac{{ - 3 + 1}}{2}or\dfrac{{ - 3 - 1}}{2}\]
On solving we get,
 \[ = \dfrac{{ - 2}}{2}or\dfrac{{ - 4}}{2}\]
On dividing we get,
 \[ = - 1or - 2\]
These are the roots or factors or we can say values of x. that is \[x = - 1 \;or\; x = - 2\]
So, the correct answer is “ \[x = - 1 \;or\; x = - 2\] ”.

Note: Note that quadratic formula is used to find the roots of a given quadratic equation. Sometimes we can factorize the roots directly. But quadratic formulas can be used generally to find the roots of any quadratic equation. The value of discriminant is used to decide the type of roots so obtained such that roots are equal or different and are real or not.