Lesson1.pdf - 2013 JKUAT SODeL JOMO KENYATTA UNIVERSITY OF AGRICULTURE TECHNOLOGY JJ II J I J DocDoc I Back Close SCHOOL OF OPEN DISTANCE AND eLEARNING

Lesson1.pdf - 2013 JKUAT SODeL JOMO KENYATTA UNIVERSITY OF...

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JKUAT SODeL 2013 JJ II J I J Doc Doc I Back Close JOMO KENYATTA UNIVERSITY OF AGRICULTURE & TECHNOLOGY SCHOOL OF OPEN, DISTANCE AND eLEARNING P.O. Box 62000, 00200 Nairobi, Kenya E-mail: [email protected] SMA 2104 Mathematics for Sciences LAST REVISION ON May 10, 2013
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JKUAT SODeL 2013 JJ II J I J Doc Doc I Back Close SMA 2104 Mathematics for Sciences This presentation is intended to covered within one week. The notes, examples and exercises should be supple- mented with a good textbook. Most of the exercises have solutions/answers appearing elsewhere and accessible by clicking the green Exercise tag. To move back to the same page click the same tag appearing at the end of the solu- tion/answer. Errors and omissions in these notes are entirely the re- sponsibility of the author who should only be contacted through the Department of Curricula & Delivery (SODeL) and suggested corrections may be e-mailed to [email protected] . JKUAT: Setting trends in higher Education, Research and Innovation 0
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JKUAT SODeL 2013 JJ II J I J Doc Doc I Back Close SMA 2104 Mathematics for Sciences LESSON 1 Quadratic equations Learning outcomes Upon completing this topic, you should be able to: Solve quadratic equations by factoring Solve quadratic equations using the method of extraction of roots Determine the nature of the solutions to a quadratic equa- tion Understand the logic underlying the method of completing the square Solve a quadratic equation using the method of completing JKUAT: Setting trends in higher Education, Research and Innovation 1
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JKUAT SODeL 2013 JJ II J I J Doc Doc I Back Close SMA 2104 Mathematics for Sciences the square Understand the derivation of the quadratic formula Solve quadratic equations using the quadratic formula JKUAT: Setting trends in higher Education, Research and Innovation 2
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JKUAT SODeL 2013 JJ II J I J Doc Doc I Back Close SMA 2104 Mathematics for Sciences 1.1. Introduction An expression of the form ax 2 + bx + c , where a, b and c are constants and x is a variable is called a quadratic expression. The highest power of x is 2. A quadratic expression is a product of two linear binomials. e.g. ( x + y )( a + b ) = ax + ay + bx + by . If the two binomials involve one variable say x i.e. They are of the form ( x + a )( x + b ), where a and b are known values. The product is ( x + a )( x + b ) = x 2 + ax + bx + ab = x 2 + x ( a + b ) + ab JKUAT: Setting trends in higher Education, Research and Innovation 3
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JKUAT SODeL 2013 JJ II J I J Doc Doc I Back Close SMA 2104 Mathematics for Sciences In this case we note that the coefficient of x in the expanded form is the sum of the constants in the factors and the term free from x is the product of the constant terms in the two factors. To factorise a quadratic expression as x 2 + px + q , one need to determine factors of q whose sum is p . Suppose these two factors are u and v .
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  • Math, Quadratic equation, Research and Innovation

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