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 functiony=x2. Here is its graph:...
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...
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....
This formula works for any quadratic equation, even the tricky ones. It’s reliable and always gives us an answer. The formula is: x = (–b ±√(b² – 4ac)) / 2a Real-life example: In gym class, you throw a basketball into the air. The height of the ball (in meters) after...
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...
Quadratic Equation Example For example, let's take the equation 2x2-6x+3=0, where a = 2, b = -6, and c = 3. D = b2 - 4ac = (-6)2-4·2·3 = 36-24 = 12 Since the discriminant is greater than zero, the equation has two real roots. These roots are found using the qua...
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...
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 ...