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

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.
  • #1
imdapolak
10
0
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
 
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  • #2


for part 'b', you would want to use the quadratic formula.
 
  • #3


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
 

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

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.

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.

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.

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.

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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