1 / 14

roots

roots. roots. roots. What are the roots of a quadratic equations ?. roots. The Roots Of Quadratic Equations. Determine whether the x value given is satisfied for the quadratic equations respectively. 2x 2 + 5x + 3 = 0 ; x = -1 (b) x 2 – 8x + 16 = 0 ; x = 4

anja
Download Presentation

roots

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. roots roots roots What are the roots of a quadratic equations ?

  2. roots

  3. The Roots Of Quadratic Equations Determine whether the x value given is satisfied for the quadratic equations respectively. • 2x2 + 5x + 3 = 0 ; x = -1 • (b)x2 – 8x + 16 = 0 ; x = 4 • (c ) x(9 – 2x) + 2 = 8 ; x = - 2 • (d)(x + 2)(x + 3) = 20 ; x = 7 2(-1)2 + 5(-1) + 3 = 2 – 5 + 3 = 0 yes (4)2 – 8(4) + 16 = 16 – 32 + 16 = 0 yes -2(9 + 4) + 2 = -26 + 2 = - 24 no (7 + 2)(7 + 3) = 9 x 10 = 90 no

  4. The roots of a quadratic equation are the values of the unknown which are satisfied the quadratic equations.

  5. Determine the roots of quadratic equations from the factorisation formed (ax + b) ( cx + d) = 0 Step 1 ax + b = 0 or cx + d = 0 Step 2 x = x = or the roots

  6. Determine the roots of quadratic equations in form of (ax + b) ( cx + d) = 0 Examples (a) (3y – 2)(y + 4) = 0 (b) 2x (x – 3) = 0 Solutions (a) (3y – 2)(y + 4) = 0 • 2x (x – 3) = 0 • 2x = 0 • x = 0 • or x – 3 = 0 • x = 3 3y – 2 = 0 y = or y + 4 = 0 y = - 4

  7. example 2 thinking process a) solve the equations (a)(i) subtract 12t from both sides of equation, factorise and solve for t (i)5t2 = 12t do not divide both sides of equation by t. you may lose one possible value of t. 5t2 = 12t 5t2 = - 12t = 0 t(5t – 12) = 0 t = 0 @ 5t – 12 = 0 t = (ii) (a)(ii)cross-multiply. Solve the quadratic equation b) Solve the equation 3x2 + 9x + 5 = 0 b) The quadratic expression is not factorisable

  8. FACTORISATION (3 TERMS) METHOD 1 : CROSS - MULTIPLICATION FACTORISED x2 + 2x – 15 = 0 -3x x - 3 x + 5 = 0 x - 3 5x + Then x + 5 x - 3 = 0 x = 3 x2 -15 2x or x + 5 = 0 The roots are x = 3 @ -5 x = - 5

  9. FACTORISATION (3 TERMS) METHOD 2 : 1 X 6 x2 + 5x + 6=0 choose 2x 3 x2 + 5x + 6 2 X 3 (+2x) +(+ 3x) = 5x Add up 2 and 3 x2 + 2x + 3x + 6 5x is changed to 2x + 3x (x2 + 2x) + (3x + 6) x(x + 2) +3(x + 2) factorise (x + 2)(x + 3) =0 Factorise again x + 2 = 0 or x + 3 = 0 x = - 2 or - 3 Two roots

  10. factorisation METHOD 3 : This abstract way of factorisation can be explained in geometry form known as Dienes’ Algebraic Experience Material

  11. Example of factorisation (3 terms ) No of big Square 1 No of rectangle 5 No. of small squares 6 example 1 : x2 + 5x + 6

  12. The arrangement: These cards are to be arranged to form a rectangle (x + 3) (x+2) (x + 3 )(x + 2) = 0 x = - 3 or - 2 The roots:

  13. closure the roots of a quadratic equation are the values of unknown which satisfied the quadratic equation

  14. solving quadratic equations ax2 + bx + c = 0 common form no factorisation yes (ax + b)(cx + d) = 0 another methods ax + b = 0 or cx + d = 0 roots x = x = or

More Related