Identify Coefficients in -8x² - 5x + 9 = 0: Component Analysis

Q: Why is the coefficient of x² equal to -8 and not 8?

The coefficient includes the sign that's directly attached to the variable term. Since we have $ -8x^2 $, the coefficient is negative eight, not positive eight.

Q: What's the difference between a coefficient and a term?

A term is the entire expression like $ -8x^2 $, while the coefficient is just the number part (-8). Think of the coefficient as the 'multiplier' of the variable.

Q: What if there's no x term in my equation?

If a term is missing, its coefficient is zero. For example, in $ -3x^2 + 7 = 0 $, there's no x term, so b = 0.

Q: Can coefficients be fractions or decimals?

Absolutely! Coefficients can be any real number - positive, negative, whole numbers, fractions, or decimals. The same identification rules apply regardless of the number type.

Standard Form Coefficients with Negative Terms

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

$-8x^2-5x+9=0$

What are the components of the equation?

❤️ 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 These are the coefficients

00:03 The coefficient of X squared is A

00:06 The coefficient of X is B

00:11 And the natural number is C

00:14 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

$-8x^2-5x+9=0$

What are the components of the equation?

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the equation is given in the standard quadratic form: $-8x^2 - 5x + 9 = 0$ .
Step 2: Determine each component:
- $a$ is the coefficient of $x^2$ , which is $-8$ .
- $b$ is the coefficient of $x$ , which is $-5$ .
- $c$ is the constant term, which is $9$ .

Now, let's resolve this using the above plan:

Step 1: The equation is already in standard form: $-8x^2 - 5x + 9 = 0$ .

Step 2: Recognize that:

$a = -8$ because it is the coefficient of $x^2$ .
$b = -5$ because it is the coefficient of $x$ .
$c = 9$ because it is the constant term.

Therefore, the components of the equation are $a = -8$ , $b = -5$ , $c = 9$ .

Final Answer

$a=-8$ $b=-5$ $c=9$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Quadratic equations follow ax² + bx + c = 0 pattern
Sign Reading: Include negative signs as part of coefficients: -8x² means a = -8
Verification: Check that ax² + bx + c reconstructs the original equation ✓

Common Mistakes

Avoid these frequent errors

Ignoring negative signs in coefficients
Don't write a = 8 when you see -8x² because you're ignoring the negative sign! This changes the entire equation's behavior and solutions. Always include the sign as part of the coefficient: a = -8.

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

Why is the coefficient of x² equal to -8 and not 8?

The coefficient includes the sign that's directly attached to the variable term. Since we have $-8x^2$ , the coefficient is negative eight, not positive eight.

What's the difference between a coefficient and a term?

A term is the entire expression like $-8x^2$ , while the coefficient is just the number part (-8). Think of the coefficient as the 'multiplier' of the variable.

How do I remember which letter represents which coefficient?

Use this pattern: a goes with the highest power (x²), b goes with the middle power (x¹), and c is the constant (no variable). It's alphabetical order matching decreasing powers!

What if there's no x term in my equation?

If a term is missing, its coefficient is zero. For example, in $-3x^2 + 7 = 0$ , there's no x term, so b = 0.

Can coefficients be fractions or decimals?

Absolutely! Coefficients can be any real number - positive, negative, whole numbers, fractions, or decimals. The same identification rules apply regardless of the number type.

🌟 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