Identify Coefficients in -x² - 2 = 0: Complete Component Analysis

Q: Why is the coefficient of x equal to 0 when there's no x term?

When a term is missing from an equation, its coefficient is 0. Think of it this way: $ -x^2 - 2 $ is really $ -x^2 + 0x - 2 $, so b = 0.

Q: How do I know which number goes with which coefficient?

Match by the power of x:a = coefficient of $ x^2 $ (highest power)b = coefficient of $ x^1 $ (middle power)c = coefficient of $ x^0 $ (constant, no x)

Q: What if the coefficient is negative like -1?

Negative coefficients are completely normal! In $ -x^2 $, the coefficient is -1, not just 1. Always include the sign as part of the coefficient.

Q: Why do we need standard form anyway?

Standard form $ ax^2 + bx + c = 0 $ makes it easy to use formulas like the quadratic formula and compare different equations consistently. It's like having a universal language for quadratic equations!

Quadratic Coefficients with Missing Linear Terms

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

$-x^2-2=0$

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 These are the coefficients

00:03 Let's write the quadratic equation formula

00:10 The coefficient of X squared is A

00:14 The coefficient of X is B

00:18 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

$-x^2-2=0$

What are the components of the equation?

Step-by-step solution

To solve this problem, we need to identify the coefficients in the quadratic equation given by $-x^2 - 2 = 0$ .

The standard form of a quadratic equation is:

$ax^2 + bx + c = 0$

In the given equation, $-x^2 - 2 = 0$ , we can write it as:

$-1 \cdot x^2 + 0 \cdot x - 2 = 0$

This corresponds to the standard form with:

Coefficient $a$ : The coefficient of $x^2$ is $-1$ .
Coefficient $b$ : The coefficient of $x$ is $0$ , as there is no $x$ term.
Coefficient $c$ : The constant term is $-2$ .

Upon examining the answer choices given, the correct choice must match these coefficients precisely.

The correct choice is:

$a = -1$ , $b = 0$ , $c = -2$

This matches Choice 3.

Final Answer

$a=-1$ $b=0$ $c=-2$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Always write as $ax^2 + bx + c = 0$
Technique: Rewrite $-x^2 - 2 = 0$ as $-1x^2 + 0x + (-2) = 0$
Check: Verify coefficients match: a = -1, b = 0, c = -2 ✓

Common Mistakes

Avoid these frequent errors

Confusing coefficients with terms
Don't write a = -x² or c = -2 as coefficient values! The coefficient is just the number part, not the variable. Always identify a = -1 (coefficient of x²), b = 0 (coefficient of x), and c = -2 (constant term).

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 x equal to 0 when there's no x term?

When a term is missing from an equation, its coefficient is 0. Think of it this way: $-x^2 - 2$ is really $-x^2 + 0x - 2$ , so b = 0.

How do I know which number goes with which coefficient?

Match by the power of x:

a = coefficient of $x^2$ (highest power)
b = coefficient of $x^1$ (middle power)
c = coefficient of $x^0$ (constant, no x)

What if the coefficient is negative like -1?

Negative coefficients are completely normal! In $-x^2$ , the coefficient is -1, not just 1. Always include the sign as part of the coefficient.

Can I rearrange the equation before identifying coefficients?

Yes, but be careful with signs! You can move terms around, but remember that moving $-2$ from the left side to the right would make it $+2$ . It's often easier to work with the equation as given.

Why do we need standard form anyway?

Standard form $ax^2 + bx + c = 0$ makes it easy to use formulas like the quadratic formula and compare different equations consistently. It's like having a universal language for quadratic equations!

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