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SUM & PRODUCT OF SECOND DEGREE EQUATIONS Flipbook PDF
SUM & PRODUCT OF SECOND DEGREE EQUATIONS
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SUM & PRODUCT SECOND DEGREE EQUATIONS By : Farha Binth Fasil XD VJHSS Nadvath Nagar
• In mathematics, a quadratic equation is a polynomial equation of the second degree. The general form is
SECOND DEGREE EQUATION
ax²+bx+c =0 • where x represents a variable or an unknown and a, b and c are constants with a ≠ 0. (If a = 0, the equation is a linear equation.) The constants a, b and c are called respectively, the quadratic coefficient, the linear coefficient and the constant term or free term.
QUADRATIC & ROOTS Quadratic: A polynomial of degree=2 y= ax²+bx+c ax² + bx +C = 0 is a quadratic equation.(a ≠ 0) * The name Quadratic comes from "quad" meaning square, because the variable gets squared (like x²). * It is also called an "Equation of Degree 2" (because of the "2" on the x)
ROOTS * A real number ‘a’ is called a root of the quadratic equation ax² + bx +c = 0,a ≠ 0 if aa² + ba² + C = 0. * If ‘a’ is a root of ax² + bx +c = 0 ,then we say that: (i) x= a satisfies the equation ax²+bx+c =0 (ii) x= a is a solution of the equation ax²+bx+c =0 * The Root of a quadratic equation ax²+bx+c =0 are called zeros of the polynomial ax²+bx+c .
Formula to find the roots of the Second degree equation
HIDDEN SECOND DEGREE EQUATIONS ! So far we have seen the "Standard Form" of a Quadratic Equation: ax² + bx +c = 0 But sometimes a quadratic equation doesn't look like that..! Here are some examples of different form:
To find the sum and product of the roots of a second degree equation…..
Look at this :
Continue.. From this, we get that For a quadratic equation ax² +bx+c = 0, the sum of its roots = –b/a the product of its roots = c/a. A quadratic equation may be expressed as a product of two binomials. ● We can find the sum and the product of the roots without finding the roots of the second degree equation.
Let's try these questions…...
We know that for a quadratic equation ax² +bx+c=0, the sum of the roots is − b/a
Find the sum of the roots of the quadratic equation: x² −5x+8=0
Here, the given quadratic equation x² −5x+8=0 is in the form ax² +bx+c=0 where a=1,b=−5 and c=8. The sum of the roots is − b/a that is:− b/a = (−5)/1 =5 Hence, sum of the roots is 5
We know that for a quadratic equation ax² +bx+c=0, the product of the roots is c/a
Find the product of the roots of the quadratic equation: x² −5x+8=0
Here, the given quadratic equation x² −5x+8=0 is in the form ax² +bx+c=0 where a=1,b=−5 and c=8. The product of the roots is c/a that is: c/a = 8/1 = 8 Hence, product of the roots is 8
BIBLIOGRAPHY ● Internet ● Secondary school mathematics ● https://www.slideshare.net/mobile/AnupMahato/q uadratic-equations-10549763