Solve the Quadratic Equation: 2x² - 10x - 12 = 0

Q: What does the discriminant tell me about the solutions?

The discriminant $ b^2-4ac $ reveals everything! If it's positive (like 196 here), you get 2 real solutions. If it's zero, you get 1 solution. If it's negative, there are no real solutions.

Q: Why do I get two different answers?

Quadratic equations naturally have two solutions because of the ± symbol in the formula. Think of it as a parabola crossing the x-axis at two points: x = 6 and x = -1.

Q: Do I always need to use the quadratic formula?

Not always! Try factoring first: $ 2x^2-10x-12 = 2(x-6)(x+1) = 0 $. If that doesn't work easily, then use the quadratic formula as your reliable backup method.

Q: What if my discriminant isn't a perfect square?

Then your solutions will have square root symbols in them! For example, if the discriminant was 50, you'd get $ \sqrt{50} = 5\sqrt{2} $ in your final answer.

Q: How can I check my work quickly?

Use the sum and product relationships! For $ ax^2+bx+c=0 $, the solutions should add to $ -\frac{b}{a} $ and multiply to $ \frac{c}{a} $. Here: 6+(-1) = 5 = -(-10)/2 ✓ and 6×(-1) = -6 = -12/2 ✓

Quadratic Formula with Integer Discriminants

Solve the following equation:

$2x^2-10x-12=0$

❤️ 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

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following equation:

$2x^2-10x-12=0$

Step-by-step solution

Let's recall the quadratic formula:

$Quadratic formula | The formula$

We'll substitute the given data into the formula:

$x={{-(-10)\pm\sqrt{-10^2-4\cdot2\cdot(-12)}\over 2\cdot2}}$

Let's simplify and solve the part under the square root:

$x={{10\pm\sqrt{100+96}\over 4}}$

$x={{10\pm\sqrt{196}\over 4}}$

$x={{10\pm14\over 4}}$

Now we'll solve using both methods, once with the addition sign and once with the subtraction sign:

$x={{10+14\over 4}} = {24\over4}=6$

$x={{10-14\over 4}} = {-4\over4}=-1$

We've arrived at the solution: X=6,-1

Final Answer

$x_1=6$ $x_2=-1$

Key Points to Remember

Essential concepts to master this topic

Formula: Use $x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$ for $ax^2+bx+c=0$
Technique: Calculate discriminant first: $(-10)^2-4(2)(-12) = 196$
Check: Substitute both solutions: $2(6)^2-10(6)-12 = 0$ and $2(-1)^2-10(-1)-12 = 0$ ✓

Common Mistakes

Avoid these frequent errors

Making sign errors when substituting negative values
Don't write -(-10) as -10 instead of +10! This gives discriminant = 100-96 = 4 instead of 100+96 = 196, leading to wrong solutions x = 3, -2. Always be extra careful with negative signs: -b means -(-10) = +10.

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 does the discriminant tell me about the solutions?

The discriminant $b^2-4ac$ reveals everything! If it's positive (like 196 here), you get 2 real solutions. If it's zero, you get 1 solution. If it's negative, there are no real solutions.

Why do I get two different answers?

Quadratic equations naturally have two solutions because of the ± symbol in the formula. Think of it as a parabola crossing the x-axis at two points: x = 6 and x = -1.

Do I always need to use the quadratic formula?

Not always! Try factoring first: $2x^2-10x-12 = 2(x-6)(x+1) = 0$ . If that doesn't work easily, then use the quadratic formula as your reliable backup method.

What if my discriminant isn't a perfect square?

Then your solutions will have square root symbols in them! For example, if the discriminant was 50, you'd get $\sqrt{50} = 5\sqrt{2}$ in your final answer.

How can I check my work quickly?

Use the sum and product relationships! For $ax^2+bx+c=0$ , the solutions should add to $-\frac{b}{a}$ and multiply to $\frac{c}{a}$ . Here: 6+(-1) = 5 = -(-10)/2 ✓ and 6×(-1) = -6 = -12/2 ✓

🌟 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