Find Coefficients in the Quadratic Equation: 5x² + 6x - 8 = 0

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

A coefficient is just the number part (like 5), while a term is the complete expression (like 5x²). When identifying coefficients, write only the numbers: a=5, not a=5x².

Q: Why is c=-8 instead of c=8?

Look carefully at the equation: $ 5x^2 + 6x - 8 = 0 $. The constant term is negative 8, so c=-8. Always include the sign when identifying coefficients!

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

If there's no x term (like $ 3x^2 - 7 = 0 $), then b=0. Every quadratic has three coefficients, even if some equal zero.

Q: Can I rearrange the equation before finding coefficients?

Yes! Just make sure it's in standard form $ ax^2 + bx + c = 0 $ first. Move all terms to one side if needed, then identify a, b, and c.

Q: What if the coefficient of x² is negative?

That's fine! If you have $ -2x^2 + 5x + 3 = 0 $, then a=-2. Just include the negative sign as part of the coefficient.

Quadratic Coefficients with Standard Form

a = coefficient of x²

b = coefficient of x

c = coefficient of the independent number

Identifies a,b,c

$5x^2+6x-8=0$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Here are the coefficients

00:03 The coefficient of X squared is A

00:06 The coefficient of X is B

00:09 And the constant term is C

00:12 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

Identifies a,b,c

$5x^2+6x-8=0$

Step-by-step solution

To identify the coefficients from the quadratic equation $5x^2 + 6x - 8 = 0$ , follow these steps:

Standard Form of Quadratic Equation: Compare $5x^2 + 6x - 8$ with the standard form $ax^2 + bx + c = 0$ .
Identify $a$ , $b$ , and $c$ :
- $a = 5$ : The coefficient of $x^2$ .
- $b = 6$ : The coefficient of $x$ .
- $c = -8$ : The constant term (independent of $x$ ).

Therefore, from the equation $5x^2 + 6x - 8 = 0$ , the coefficients are identified as $a=5$ , $b=6$ , and $c=-8$ .

Comparing with choices, we find that choice 2 is correct: $a=5$ , $b=6$ , $c=-8$ .

Thus, the coefficients are identified as $a=5$ , $b=6$ , $c=-8$ .

Final Answer

$a=5$ $b=6$ $c=-8$

Key Points to Remember

Essential concepts to master this topic

Standard Form: Match $ax^2 + bx + c = 0$ with given equation
Technique: Identify each position: a=5, b=6, c=-8 from $5x^2 + 6x - 8 = 0$
Check: Verify signs carefully: constant -8 gives c=-8, not c=8 ✓

Common Mistakes

Avoid these frequent errors

Including variables in coefficient values
Don't write a=5x² or b=6x = wrong format! These are terms, not coefficients. The coefficient is just the number part. Always identify a=5, b=6, c=-8 as pure numbers only.

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

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

A coefficient is just the number part (like 5), while a term is the complete expression (like 5x²). When identifying coefficients, write only the numbers: a=5, not a=5x².

Why is c=-8 instead of c=8?

Look carefully at the equation: $5x^2 + 6x - 8 = 0$ . The constant term is negative 8, so c=-8. Always include the sign when identifying coefficients!

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

If there's no x term (like $3x^2 - 7 = 0$ ), then b=0. Every quadratic has three coefficients, even if some equal zero.

Can I rearrange the equation before finding coefficients?

Yes! Just make sure it's in standard form $ax^2 + bx + c = 0$ first. Move all terms to one side if needed, then identify a, b, and c.

What if the coefficient of x² is negative?

That's fine! If you have $-2x^2 + 5x + 3 = 0$ , then a=-2. Just include the negative sign as part of the coefficient.

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