Q: How do you solve a quadratic equation?

Quadratic equations can be solved using several methods: a) Factorization: Express the quadratic expression as the product of two binomials. b) Completing the Square: Convert the quadratic into a perfect square trinomial. c) Quadratic Formula: Use the formula x = {-b ± √(b2 - 4ac)}/2a to find the roots. d) Graphical Method: Plot the equation on a graph and find where it intersects the x-axis (if applicable).

Q: What is the quadratic formula?

The quadratic formula is used to solve any quadratic equation and is given by: x = {-b ± √(b2 - 4ac)}/2a It provides the solutions for x in terms of the coefficients a, b, and c.

Q: What are real and complex roots?

Real roots occur when the discriminant D≥0, meaning the quadratic equation has solutions that are real numbers. Complex roots occur when D<0, meaning the solutions involve imaginary numbers.

Q: Can a quadratic equation have only one solution?

Yes, a quadratic equation can have one solution when the discriminant D=0. In this case, the equation has a repeated or double root.

Q: What is the graph of a quadratic equation?

The graph of a quadratic equation is a parabola. If the coefficient a>0, the parabola opens upwards. If a<0, the parabola opens downwards. The points where the parabola crosses the x-axis (if any) represent the roots of the equation.

Question 1

What is a quadratic equation?

Accepted Answer

A quadratic equation is a polynomial equation of degree 2. It is written in the standard form:
ax2 + bx + c = 0, where a, b, and c are real numbers, and a ≠ 0.

Question 2

What is the degree of a quadratic equation?

Accepted Answer

The degree of a quadratic equation is 2 because the highest power of the variable x is 2.

Question 3

How do you find the degree of a polynomial?

Accepted Answer

A: The degree of a polynomial is the highest power of the variable in the expression. For example, in P(x) = 4x3 + 2x2 + 5x + 7, the degree is 3.

Question 4

How many solutions can a quadratic equation have?

Accepted Answer

A quadratic equation can have two solutions, which are called the roots of the equation. Depending on the discriminant, it may have:
1. Two distinct real roots,
2. One repeated real root,
3. No real roots (complex roots).

Question 5

What is the discriminant in a quadratic equation?

Accepted Answer

For a quadratic equation ax2 + bx + c = 0, Discriminant is given by the formula:
D = b2 - 4ac
If D > 0: there are two distinct real roots.
If D < 0: there are no real roots (the roots are complex).
If D = 0: there is one real repeated root.

Question 6

How do you solve a quadratic equation?

Accepted Answer

Quadratic equations can be solved using several methods:
a) Factorization: Express the quadratic expression as the product of two binomials.
b) Completing the Square: Convert the quadratic into a perfect square trinomial.
c) Quadratic Formula: Use the formula x = {-b ± √(b2 - 4ac)}/2a to find the roots.
d) Graphical Method: Plot the equation on a graph and find where it intersects the x-axis (if applicable).

Question 7

What is the quadratic formula?

Accepted Answer

The quadratic formula is used to solve any quadratic equation and is given by:
x = {-b ± √(b2 - 4ac)}/2a
It provides the solutions for x in terms of the coefficients a, b, and c.

Question 8

What are real and complex roots?

Accepted Answer

Real roots occur when the discriminant D≥0, meaning the quadratic equation has solutions that are real numbers.
Complex roots occur when D<0, meaning the solutions involve imaginary numbers.

Question 9

Can a quadratic equation have only one solution?

Accepted Answer

Yes, a quadratic equation can have one solution when the discriminant D=0. In this case, the equation has a repeated or double root.

Question 10

What is the graph of a quadratic equation?

Accepted Answer

The graph of a quadratic equation is a parabola. If the coefficient a>0, the parabola opens upwards. If a<0, the parabola opens downwards. The points where the parabola crosses the x-axis (if any) represent the roots of the equation.

Question 11

What are the applications of quadratic equations?

Accepted Answer

Quadratic equations are used in various real-life applications such as
calculating areas,
determining the trajectory of objects,
solving problems in physics (e.g., motion under gravity),
optimizing business models, and financial calculations.

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