Finding Roots of x² + 5x + 4: Quadratic Equation Solution

Q: Can I solve this by factoring instead of using the quadratic formula?

Yes! Since $ x^2+5x+4 = (x+1)(x+4) $, you can set each factor equal to zero: x+1=0 gives x=-1, and x+4=0 gives x=-4.

Q: Why are both roots negative?

Look at the original equation: $ x^2+5x+4=0 $. Since b=+5 is positive and c=+4 is positive, both roots must be negative to make the sum and product work out correctly.

Q: How do I know which method to use - factoring or quadratic formula?

Try factoring first if the coefficients are small integers. If you can't factor easily in 30 seconds, use the quadratic formula - it always works!

Q: What does the discriminant tell me?

The discriminant $ b^2-4ac = 25-16 = 9 $ is a perfect square, which means you'll get two distinct rational roots. If it's negative, there are no real solutions.

Q: Why do we write ± in the quadratic formula?

The ± symbol gives us both solutions at once! $ \frac{-5+3}{2} = -1 $ and $ \frac{-5-3}{2} = -4 $. Every quadratic equation has exactly two solutions (counting multiplicity).

Quadratic Factoring with Integer Solutions

Solve the following equation:

$x^2+5x+4=0$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:03 Pay attention to the coefficients

00:13 Use the roots formula

00:22 Substitute appropriate values according to the given data and solve for X

00:42 Calculate the products and square

00:52 Calculate the square root of 9

01:00 Find the 2 possible solutions

01:08 This is one solution

01:15 And this is the second solution, and the answer to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following equation:

$x^2+5x+4=0$

Step-by-step solution

The parameters are expressed in the quadratic equation as follows:

aX2+bX+c=0

We substitute into the formula:

-5±√(5²-4*1*4)
2

-5±√(25-16)
2

-5±√9
2

-5±3
2

The symbol ± means that we have to solve this part twice, once with a plus and a second time with a minus,

This is how we later get two results.

-5-3 = -8
-8/2 = -4

-5+3 = -2
-2/2 = -1

And thus we find out that X = -1, -4

Final Answer

$x_1=-1$ $x_2=-4$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Identify coefficients a=1, b=5, c=4 in ax²+bx+c=0
Quadratic Formula: $x = \frac{-5 ± \sqrt{25-16}}{2} = \frac{-5 ± 3}{2}$
Check Roots: Substitute x=-1 and x=-4: (-1)²+5(-1)+4=0 ✓

Common Mistakes

Avoid these frequent errors

Sign errors when applying the quadratic formula
Don't forget the negative sign in front of b = wrong signs in final answer! Students often write +5 instead of -5, getting positive roots instead of negative ones. Always write -b first, so -(+5) = -5 in the numerator.

Practice Quiz

Test your knowledge with interactive questions

a = Coefficient of x²

b = Coefficient of x

c = Coefficient of the independent number

what is the value of $$ a $$ in the equation

$$ y=3x-10+5x^2 $$

FAQ

Everything you need to know about this question

Can I solve this by factoring instead of using the quadratic formula?

Yes! Since $x^2+5x+4 = (x+1)(x+4)$ , you can set each factor equal to zero: x+1=0 gives x=-1, and x+4=0 gives x=-4.

Why are both roots negative?

Look at the original equation: $x^2+5x+4=0$ . Since b=+5 is positive and c=+4 is positive, both roots must be negative to make the sum and product work out correctly.

How do I know which method to use - factoring or quadratic formula?

Try factoring first if the coefficients are small integers. If you can't factor easily in 30 seconds, use the quadratic formula - it always works!

What does the discriminant tell me?

The discriminant $b^2-4ac = 25-16 = 9$ is a perfect square, which means you'll get two distinct rational roots. If it's negative, there are no real solutions.

Why do we write ± in the quadratic formula?

The ± symbol gives us both solutions at once! $\frac{-5+3}{2} = -1$ and $\frac{-5-3}{2} = -4$ . Every quadratic equation has exactly two solutions (counting multiplicity).

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Solving Quadratic Equations questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime