Identify Coefficients in 10x²+20x+5=0: Finding a, b, and c Values

Q: Why does the order of terms matter when finding coefficients?

The standard form $ ax^2 + bx + c = 0 $ has a specific order. Coefficients a, b, and c correspond to specific positions, so you must rearrange terms first to avoid mixing them up.

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

If there's no $ x $ term, then b = 0. For example, in $ 3x^2 + 7 = 0 $, we have a = 3, b = 0, and c = 7.

Q: What if there's no constant term?

If there's no constant term, then c = 0. For example, in $ 2x^2 + 5x = 0 $, we have a = 2, b = 5, and c = 0.

Q: How do I handle negative coefficients?

Include the negative sign as part of the coefficient! In $ -3x^2 + 4x - 1 = 0 $, we have a = -3, b = 4, and c = -1.

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

A coefficient is just the number part, while a term includes the variable. For $ 10x^2 $, the coefficient is 10 and the term is $ 10x^2 $.

Quadratic Coefficients with Rearranged Terms

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

$10x^2+5+20x=0$

What are the components of the equation?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Identify the equation components

00:03 Let's write the quadratic equation pattern

00:08 The coefficient of X squared is A

00:13 The coefficient of X is B

00:19 And the constant term is C

00:22 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

$10x^2+5+20x=0$

What are the components of the equation?

Step-by-step solution

To determine the components of the quadratic equation, follow these steps:

Step 1: Recognize the standard form of a quadratic equation, which is $ax^2 + bx + c = 0$ .
Step 2: Compare the given equation $10x^2 + 20x + 5 = 0$ to the standard form.
Step 3: Identify the coefficients:
- The term $10x^2$ indicates that $a = 10$ .
- The term $20x$ indicates that $b = 20$ .
- The term $5$ is the constant term, so $c = 5$ .

Therefore, the components of the equation are:

$a = 10$ , $b = 20$ , $c = 5$ .

The correct answer among the choices provided is the one that correctly identifies these coefficients:

$a=10$ $b=20$ $c=5$

Therefore, the correct choice is Choice 4.

Final Answer

$a=10$ $b=20$ $c=5$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Always rearrange to $ax^2 + bx + c = 0$ first
Technique: From $10x^2 + 5 + 20x = 0$ write as $10x^2 + 20x + 5 = 0$
Check: Verify a=10, b=20, c=5 by matching each term's coefficient ✓

Common Mistakes

Avoid these frequent errors

Taking coefficients from equation without rearranging to standard form
Don't read coefficients directly from $10x^2 + 5 + 20x = 0$ = wrong b and c values! The terms must be in order first. Always rearrange to $ax^2 + bx + c = 0$ before identifying coefficients.

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 does the order of terms matter when finding coefficients?

The standard form $ax^2 + bx + c = 0$ has a specific order. Coefficients a, b, and c correspond to specific positions, so you must rearrange terms first to avoid mixing them up.

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

If there's no $x$ term, then b = 0. For example, in $3x^2 + 7 = 0$ , we have a = 3, b = 0, and c = 7.

What if there's no constant term?

If there's no constant term, then c = 0. For example, in $2x^2 + 5x = 0$ , we have a = 2, b = 5, and c = 0.

How do I handle negative coefficients?

Include the negative sign as part of the coefficient! In $-3x^2 + 4x - 1 = 0$ , we have a = -3, b = 4, and c = -1.

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

A coefficient is just the number part, while a term includes the variable. For $10x^2$ , the coefficient is 10 and the term is $10x^2$ .

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