Solve the following equation:
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Solve the following equation:
To solve the quadratic equation , we will apply the quadratic formula.
Given the quadratic equation is of the form , we identify:
Next, we use the quadratic formula:
Calculate the discriminant:
Since the discriminant is positive, we have two real solutions.
Now, plug the values into the quadratic formula:
Solving for the two values of :
Therefore, the solutions to the equation are and .
a = Coefficient of x²
b = Coefficient of x
c = Coefficient of the independent number
what is the value of \( a \) in the equation
\( y=3x-10+5x^2 \)
The discriminant tells you how many solutions exist! If it's positive (like 100 here), you get two real solutions. If zero, one solution. If negative, no real solutions.
That's exactly when the quadratic formula is your best friend! Some quadratics like don't factor nicely, but the formula always works.
Try this song: "x equals negative b, plus or minus the square root, of b squared minus 4ac, all over 2a!" Practice writing several times.
Quadratic equations create parabolas that can cross the x-axis at two points! Each crossing point is a solution, so and are both correct.
Optional but helpful! You could divide everything by 2 to get , making the numbers smaller and easier to work with.
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