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15 Questions

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Master Quadratic Equations

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Questions and Answers

Which of the following equations is a quadratic equation?

$5x^3 - 2x^2 + x - 3 = 0$

$x^2 + 3x - 2 = 0$ (correct)

$2x + 4y = 6$

$3x + 2 = 0$

What are the solutions of a quadratic equation?

Double roots

Complex solutions

Roots or zeros (correct)

Real numbers

How many solutions does a quadratic equation have?

At most one solution

At most two solutions (correct)

At most three solutions

At most four solutions

If all the coefficients of a quadratic equation are real numbers, what are the possible types of solutions?

All of the above Signup and view all the answers

Does a quadratic equation always have two roots?

Yes Signup and view all the answers

What is the standard form of a quadratic equation?

$ax^2 + bx + c = 0$ Signup and view all the answers

What are the coefficients of a quadratic equation?

The coefficients are the values of a, b, and c in the equation. Signup and view all the answers

What is the difference between a linear equation and a quadratic equation?

A linear equation has a power of 1 for the variable, while a quadratic equation has a power of 2 for the variable. Signup and view all the answers

What are the possible types of solutions for a quadratic equation with real coefficients?

There can be two real solutions, a single real double root, or two complex solutions that are complex conjugates of each other. Signup and view all the answers

How many roots does a quadratic equation always have?

A quadratic equation always has two roots, if complex roots are included. Signup and view all the answers

What is the general form of a quadratic equation?

$ax^2 + bx + c = 0$ Signup and view all the answers

What are the possible types of solutions for a quadratic equation with real coefficients?

There are either two real solutions, or a single real double root, or two complex solutions that are complex conjugates of each other. Signup and view all the answers

How many solutions does a quadratic equation have?

A quadratic equation has at most two solutions. Signup and view all the answers

What are the coefficients of a quadratic equation?

The coefficients of a quadratic equation are the quadratic coefficient (a), the linear coefficient (b), and the constant coefficient or free term (c). Signup and view all the answers

What are the roots of a quadratic equation?

The values of x that satisfy the equation are called solutions of the equation, and roots or zeros of the expression on its left-hand side. Signup and view all the answers