25+-+Sec.+9.5

nSection 9.5 Section 9.5 Problem Solving Using the Discriminant By Jessica Quinn, Sam Kim and Kalyn Gajeski

** The discriminant can be used to find the number of solutions of a Quadratic Equation.

The Quadratic Formula has an expression b 2 -4ac and it is the discriminant. ** **

For example: x 2 -2x+3=0 By using the Discriminant (-2) 2 -4(1)(3)=-8 The Number of solutions are: zero The Quadratic equation crosses the x-axis 2-positive, 1-zero and o-negative x intercepts . 

Problem Solving Using the Discriminant ** Extra Problem Link

Example 1 x //** ² **// +3x=18 a: 1 b: 3 c: -18 3^2 - 4(1)(-18) = 9 - //**
 * // Worked Out examples!

**// 0= X2+8X-33 0= (X+11)(x-3) x+11=0 or x-3=0 x=-11 or x=3 //** x //** ² **// +4x+5 4 2 -4(1)(5)=16-20=-4 There are no x-intercepts. //**
 * // Sample Problems!

Example 3) x 2 + 2x - 4 = 0 **// a: 1 b: 2 c: -4 (-4) //** 2 **// - (4)(1)(-4)  The answer is positive so there are TWO x-intercepts.

Good Luck! Trying to find the number of solutions of a Quadratic Equation For example: ax2+bx+c=0 Four practice examples //** Use the discriminant to determine haw many x-intercepts there are. solve for x

 x ² // - //2x+8=0

x 2 -2x+3=0

x 2 -2x+1=0

x <span style="color: #8c31e3; font-family: 'Arial Black',Gadget,sans-serif; vertical-align: super;">2 <span style="color: #ff00ff; font-family: 'Arial Black',Gadget,sans-serif;">-2x-2=0