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© Mr. Sims Algebra 2 Section 3.5 Quadratic Equations Equations such as: 5x2 + 8x – 12 = 0 , 9x2 – 25 = 0, and 3x2 + 4x = 0 are called quadratic equations. Each equation contains a polynomial of the second degree (exponent of 2). The standard form of a quadratic equation is: ax2 + bx + c = 0, where a,b, and c are numbers and (a 0). Examples: 3x2 + 5x + 6 = 0 or x2 – 2x + 1 = 0 One way to solve a quadratic equation is to: - write the equation in standard form {ax2 + bx + c = 0} - factor it - and set each factor equal to 0 © Mr. Sims Solve each equation. 1. x2 – 13x + 40 = 0 (x – 8)(x – 5) = 0 factor into 2 binomials x – 8 = 0 or x – 5 = 0 set each factor equal to 0 +8 +8 x=8 +5 +5 or x=5 2. 0 = x2 + 15x + 50 x2 + 15x + 50 = 0 switch around (x + 10)(x + 5) = 0 factor into 2 binomials x + 10 = 0 or x + 5 = 0 set each factor equal to 0 -10 -10 x = -10 -5 or -5 x = -5 © Mr. Sims 3. 6 = b2 – b -6 -6 subtract 6 to get in standard form b2 – b – 6 = 0 standard form (b – 3)(b + 2) = 0 factor into 2 binomials b – 3 = 0 or b + 2 = 0 set each factor equal to 0 -2 -2 +3 +3 b=3 or b = -2 4. 2a2 – 10a = 0 2a(a – 5) = 0 factor 2a out 2a = 0 or a – 5 = 0 set each factor equal to 0 +5 +5 a=0 or a=5 © Mr. Sims 5. 15a = a2 -15a -15a subtract 15a from both sides a2 – 15a = 0 a(a – 15) = 0 factor a out a = 0 or a – 15 = 0 set each factor equal to 0 +15 +15 or a = 15 6. 0 = c2 – 36 c2 – 36 = 0 switch around (c + 6)(c – 6) = 0 c2 – 36 is a difference of 2 squares: c + 6 = 0 or c – 6 = 0 set each factor equal to 0 -6 +6 +6 -6 c = -6 a2 – b2 = (a + b)(a – b) or c=6 © Mr. Sims 7. x4 – 26x2 + 25 = 0 (x2 – 25)(x2 – 1) = 0 factor into 2 binomials x2 – 25 = 0 or x2 – 1 = 0 set each factor equal to 0 both of these are a difference of 2 squares: a2 – b2 = (a + b)(a – b) (x + 5)(x – 5) = 0 or (x + 1)(x – 1) = 0 x + 5 = 0 or x – 5 = 0 x + 1 = 0 or x – 1 = 0 -5 -5 +5 +5 -1 -1 +1 +1 x = -5 or x = 5 x = -1 or x = 1 x = -5, 5, -1, 1 © Mr. Sims 8. 900 + x4 = 109x2 -109x2 -109x2 x4 – 109x2 + 900 = 0 (x2 – 100)(x2 – 9) = 0 x2 – 100 = 0 or x2 – 9 = 0 (x + 10)(x – 10) = 0 (x + 3)(x – 3) = 0 x + 10 = 0 or x – 10 = 0 x + 3 = 0 or x – 3 = 0 x = -10 or x = 10 x = -3 or x = 3 x = -10, 10, -3, 3 © Mr. Sims Solve each equation. 1.) a2 – a – 42 = 0 2.) y2 = 12 – y 3.) 6y = 16 – y2 4.) 3x2 = -12x 5.) z2 – 64 = 0 6.) 16 = z2 Algebra 2 Section 3.5 Assignment 7.) a4 – 29a2 + 100 = 0 © Mr. Sims Any rebroadcast, reproduction, or other use of the pictures and materials from this site and presentations, without the express written consent of Mr. Sims, is prohibited. © Mr. Sims. All rights reserved. © Mr. Sims