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chwala
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- Homework Statement
- Kindly see the attached problem below
- Relevant Equations
- sum and products of roots of a quadratic equation
Where does that combination come from? Did you mean α=β=3?chwala said:i should be correct, checking with a previous example...
View attachment 280707
if i let ##∝=3## and ##β=1##,
haruspex said:Where does that combination come from? Did you mean α=β=3?
Btw, ∝ means "is proportional to". It is not a form of α (or in LaTeX, α).
A quadratic equation is an equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. It represents a parabola when graphed and can have two solutions, or roots, when solved.
The roots of a quadratic equation can be found by using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a. This formula can be used when the equation is in standard form, or by factoring the equation and setting each factor equal to 0.
No, a quadratic equation can only have a maximum of two roots. This is because a quadratic equation is a second-degree polynomial and the Fundamental Theorem of Algebra states that a polynomial of degree n can have at most n roots.
A quadratic equation has real roots if the discriminant, b^2 - 4ac, is greater than or equal to 0. If the discriminant is less than 0, the equation will have imaginary roots. The square root of a negative number is not a real number, so the roots will be in the form of a complex number.
Yes, the roots of a quadratic equation can be irrational numbers. This means that the roots cannot be expressed as a fraction or decimal and will have an infinite number of non-repeating digits after the decimal point. For example, the roots of x^2 - 2 = 0 are ±√2, which are irrational numbers.