# What Are the Solutions to bx^2 + cx + a = 0 for Any Constants a, b, and c?

• imdapolak
In summary, for part a, the values of x that make y=0 are given by the quadratic formula, which is (-c ± √(c^2-4ab)) / 2b. For part b, when a=3.1, b=-2.2, and c=-4.3, the solutions to the equation are approximately 2.037 and -0.562.
imdapolak
1. Suppose y = bx^2 +cx + a
a.) in terms of a, b, and c, what values of x make y=0?

b.) if a=3.1, b= -2.2 and c=-4.3 evaluate those solutions to 3 significant digits:

## Homework Equations

3. I am not really sure how to solve for what the question is asking for in part a, and for part b do I just plug those values into a quadratic formula for an answer? Any help is appreciated

for part 'b', you would want to use the quadratic formula.

Part a is really very similar to part b, it is just a much more general case, which applies to any constants a, b and c. It is basically saying that for any given constants, what are the solutions to the equation:

bx^2 +cx + a = 0

## 1. What is a quadratic equation?

A quadratic equation is a polynomial equation of the second degree, meaning the highest power of the variable is 2. It is in the form of ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable.

## 2. How do you solve a quadratic equation?

There are several methods for solving a quadratic equation, but the most commonly used is the quadratic formula. This formula is x = (-b ± √(b^2-4ac)) / 2a. You can also solve it by factoring, completing the square, or graphing.

## 3. What are the solutions to a quadratic equation?

A quadratic equation can have either two real solutions, two complex solutions, or one double root. The number of solutions depends on the discriminant (b^2-4ac) of the equation.

## 4. Can all quadratic equations be solved?

Yes, all quadratic equations can be solved using the quadratic formula. However, some equations may have imaginary or complex solutions.

## 5. How is solving a quadratic equation helpful in real life?

Quadratic equations are used to model real life situations such as projectile motion, maximizing profits, and finding the minimum or maximum of a curved shape. They are also used in engineering, physics, and economics.

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