Identify Coefficients in the Quadratic Equation: x²+4x-5=0

Q: Why is the coefficient of x² equal to 1 when I don't see any number?

When no number appears before a variable, the coefficient is always 1. Think of it like this: $ x^2 $ is the same as writing $ 1 \cdot x^2 $!

Q: What if the constant term is negative like -5?

The sign is part of the coefficient! In $ x^2 + 4x - 5 = 0 $, the constant term is -5, so $ c = -5 $, not $ c = 5 $.

Q: How do I remember which coefficient is which?

Use this pattern: $ ax^2 + bx + c = 0 $a goes with $ x^2 $ (highest power)b goes with $ x $ (middle power)c is the constant (no variable)

Q: What if the equation isn't in standard form?

First, rearrange the equation so all terms are on one side equal to zero. Then identify coefficients from the $ ax^2 + bx + c = 0 $ pattern.

Q: Can any of the coefficients be zero?

Yes! b or c can be zero, but a cannot be zero (otherwise it wouldn't be quadratic). For example, in $ 2x^2 - 8 = 0 $, we have $ b = 0 $.

Quadratic Coefficients with Standard Form

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

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

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 The coefficient of X squared is A

00:06 The coefficient of X is B

00:11 and the natural number is C

00:16 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

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

What are the components of the equation?

Step-by-step solution

The quadratic equation we have is $x^2 + 4x - 5 = 0$ .

We'll compare this with the general form of a quadratic equation: $ax^2 + bx + c = 0$ .

1. Identify $a$ : The coefficient of $x^2$ in the given equation is $1$ . Therefore, $a = 1$ .

2. Identify $b$ : The coefficient of $x$ in the given equation is $4$ . Therefore, $b = 4$ .

3. Identify $c$ : The constant term in the given equation is $-5$ . Therefore, $c = -5$ .

Thus, the components of the equation are:

$a = 1$
$b = 4$
$c = -5$

The correct answer to this problem, matching choice id 3, is:

$a=1$ $b=4$ $c=-5$

Final Answer

$a=1$ $b=4$ $c=-5$

Key Points to Remember

Essential concepts to master this topic

Standard Form: General quadratic equation is $ax^2 + bx + c = 0$
Coefficient Recognition: For $x^2 + 4x - 5 = 0$ , identify each number multiplying variables
Check: Verify $a = 1$ , $b = 4$ , $c = -5$ match pattern ✓

Common Mistakes

Avoid these frequent errors

Missing coefficient of 1
Don't assume $a = 0$ when you see $x^2$ = wrong coefficients! When no number appears before $x^2$ , the coefficient is 1, not 0. Always remember that $x^2 = 1 \cdot x^2$ .

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 1 when I don't see any number?

When no number appears before a variable, the coefficient is always 1. Think of it like this: $x^2$ is the same as writing $1 \cdot x^2$ !

What if the constant term is negative like -5?

The sign is part of the coefficient! In $x^2 + 4x - 5 = 0$ , the constant term is -5, so $c = -5$ , not $c = 5$ .

How do I remember which coefficient is which?

Use this pattern: $ax^2 + bx + c = 0$

a goes with $x^2$ (highest power)
b goes with $x$ (middle power)
c is the constant (no variable)

What if the equation isn't in standard form?

First, rearrange the equation so all terms are on one side equal to zero. Then identify coefficients from the $ax^2 + bx + c = 0$ pattern.

Can any of the coefficients be zero?

Yes! b or c can be zero, but a cannot be zero (otherwise it wouldn't be quadratic). For example, in $2x^2 - 8 = 0$ , we have $b = 0$ .

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