Quadratic Equation

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Quadratic Equation By 10 ‘C’ Students

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What is A Quadratic Equation A Quadratic Equation in Standard Form (a, b, and c can have any value, except that a can't be 0.) The letters a, b and c are coefficients. The letter "x" is the variable or unknown

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For Example this makes it a quadratic The name Quadratic comes from "quad" meaning square, because of x 2 (in other words x squared ). It can also be called an equation of degree 2.

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Some othe r Example Where a=2, b=5 and c=3 This one is a little more tricky: Where is a ? In fact a=1 , because we don't usually write "1x 2 " b=-3 And where is c ? Well, c=0 , so is not shown.

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We can solve Quadratic equation by 3 methods: 1:BY FACTORISATION METHOD 2: BY COMPLETING THE SQUARE METHOD 3:BY QUADRATIC FORMULA

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Solving Quadratic Equations by Factorisation method

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Solving Quadratic Equations by Factorisation This presentation is an introduction to solving quadratic equations by factorisation. The following idea is used when solving quadratics by factorisation. If the product of two numbers is 0 then one (or both) of the numbers must be 0. So if xy = 0 either x = 0 or y = 0 Considering some specific numbers: If 8 x x = 0 then x = 0 If y x 15 = 0 then y = 0

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Solving Quadratic Equations by Factorisation a x 2 + b x + c = 0 , a  0 Some quadratic equations can be solved by factorising and it is normal to try this method first before resorting to the other two methods discussed. The first step in solving is to rearrange them (if necessary) into the form shown above. x 2 = 4 x Example 1: Solve x 2 – 4 x = 0 x ( x – 4) = 0 either x = 0 or x – 4 = 0 if x – 4 = 0 then x = 4 Solutions (roots) are x = 0 , x = 4 rearrange factorise

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6 x 2 = – 9 x Example 2: Solve 6 x 2 + 9 x = 0 3 x (2 x + 3) = 0 either 3 x = 0 or 2 x + 3 = 0  x = 0 or x = – 1½ rearrange factorise

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Solving Quadratic Equations by Completing the Square

Creating a Perfect Square Trinomial:

Creating a Perfect Square Trinomial In the following perfect square trinomial, the constant term is missing. x 2 + 14x + ____ Find the constant term by squaring half the coefficient of the linear term. (14/2) 2 x 2 + 14x + 49

Solving Quadratic Equations by Completing the Square:

Solving Quadratic Equations by Completing the Square Solve the following equation by completing the square: Step 1: Move quadratic term, and linear term to left side of the equation

Solving Quadratic Equations by Completing the Square:

Solving Quadratic Equations by Completing the Square Step 2: Find the term that completes the square on the left side of the equation. Add that term to both sides.

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Solving Quadratic Equations by Completing the Square Step 3: Factor the perfect square trinomial on the left side of the equation. Simplify the right side of the equation.

Solving Quadratic Equations by Completing the Square:

Solving Quadratic Equations by Completing the Square Step 4: Take the square root of each side

Solving Quadratic Equations by Completing the Square:

Solving Quadratic Equations by Completing the Square Step 5: Set up the two possibilities and solve

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Solving Quadratic Equations by Quadratic formula

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The Quadratic Formula.

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What Does The Formula Do ? The Quadratic formula allows you to find the roots of a quadratic equation (if they exist) even if the quadratic equation does not factorise. The formula states that for a quadratic equation of the form : ax 2 + bx + c = 0 The roots of the quadratic equation are given by :

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Example 1 Use the quadratic formula to solve the equation : x 2 + 5x + 6= 0 Solution: x 2 + 5x + 6= 0 a = 1 b = 5 c = 6

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x = - 2 or x = - 3 These are the roots of the equation.

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Thank you Made And Presented By Amar Abhishek Rawat Abhishek Solanki Abhishek Sharma Ajay Anirudh