Answer: x = 2 ± 1.5i The graph does not cross the x-axis. That is why we ended up with complex numbers. BUT an upside-down mirror image of our equation does cross the x-axis at 2± 1.5 (note: missing the i). Just an interesting fact for you!Summary...
Answer: Therefore the maximum height attained is 36m. Example 3: Find the quadratic equation having the roots 5 and 8 respectively. Solution: The quadratic equation having the roots α, β, is x2 - (α + β)x + αβ = 0. Given α = 5, and β = 8. Therefore the quadratic equatio...
Understanding the properties of a quadratic equation and how to recognize them when written out, it is natural to wonder what a quadratic equation looks like when graphed? That's a great question! To answer this, consider the simplest quadratic equation, the function {eq}y = x^2 {/eq}. ...
With the quadratic equation in this form:Step 1: Find two numbers that multiply to give ac (in other words a times c), and add to give b.Example: 2x2 + 7x + 3 ac is 2×3 = 6 and b is 7 So we want two numbers that multiply together to make 6, and add up to 7 In fact...
Understanding the properties of a quadratic equation and how to recognize them when written out, it is natural to wonder what a quadratic equation looks like when graphed? That's a great question! To answer this, consider the simplest quadratic equation, the function {eq}y = x^2 {/eq}. ...
Example 2. c = 0. Solve this quadratic equation:ax² + bx = 0Solution. Since there is no constant term: c = 0, x is a common factor:x(ax + b) = 0. This implies: x = 0 or x = − ba .Those are the two roots.Problem 4. Find the roots of each quadratic....
It is usual to write a quadratic equation with the right-hand side equal to zero. To solve it, you first factorise the left-hand side if possible, and this requires a particular technique. Quadratic factorisation Example1.21 Factorisexa+xb+ya+yb ...
Example-3:\({x^2} + 2x + 2 = 0\) It is of the form \(a{x^2} + bx + c = 0\). Therefore, it is a quadratic equation. What are the Roots of Quadratic Equation? In general, a real number \(\alpha \) is called a root of the quadratic equation \(a{x^2} + bx + c...
Ask a question Our experts can answer your tough homework and study questions. Ask a question Search AnswersLearn more about this topic: Quadratic Equation | Definition, Formula & Examples from Chapter 14 / Lesson 1 307K What is a quadratic equation? Learn what makes an equation quadratic...
Fortunately, the answer simple and well-known: The quadratic equation gets its solutions using the following quadratic formula \[x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\] The values obtained with this equation are known as the roots of the quadratic equation (also known as solutions...