MATHS 2/10-QUADRATIC EQUATIONS : MATHS 2/10-QUADRATIC EQUATIONS BY MANJULA B
manjulab64@gmail.com
MATHS- 2/10 : MATHS- 2/10 THIS SESSION RUNS FOR 60 MINUTES
PLEASE ENSURE YOUR SOUND SETTINGS
THIS IS AN AUDIO CLASS ONLY
ANY TECHNICAL PROBLEMS LIKE AUDIO DISTURBANCES, POWER CUTS AND INTERNET PROBLEMS ARE BEYOND MY CONTROL. I WILL TRY TO RESCHEDULE WHERVER NECESSARY
LAST TEN MINUTES DEVOTED FOR YOUR DOUBTS
MORE DETAILS : email anytime manjulab64@gmail.com
QUADRATIC EQUATIONS : QUADRATIC EQUATIONS An equation involving a variable root of degree2 is a Quadratic Equation as against a variable of one degree which is a linear equation
A quadratic equation has two roots
A quadratic equation involving a variable only in second degree is a pure quadratic equation
Ex: x2 - 5, 3x2 = 16
An equation that can be expressed in the form of ax2+c = 0, where a and c are real numbers and a is not equal to zero is a pure quadratic equation
QUADRATIC EQUATIONS-CONTD : QUADRATIC EQUATIONS-CONTD A quadratic equation involving a variable in second degree as well as in first degree is an adfected quadratic equation Ex : x2+x-2=0, 2a2 - 3a = 4
The standard form of quadratic equation is ax2+bx+c =0, where a,b,c are constants, a is not equal to zero
Quadratic equations can be solved by factorisation
MEMORISE THESE BY HEART : MEMORISE THESE BY HEART The roots of quadratic equation is given by the formula x = -b +or - vb2-4ac/2a, where b2-4ac is know as discriminant and is denoted by ?
The discriminant b2-4ac decides the nature of roots
If > 0, the roots are real and distinct
If = 0, the roots are real and equal
If < 0, the roots are imaginary
For the quadratic equation, sum of the roots is -b/a and products of the root is c/a
QUADRATIC EQUATIONS-CONTD : QUADRATIC EQUATIONS-CONTD The roots are equal and opposite if b = 0
The roots are reciprocals of each other if c = a
The equation whose roots are m and n is x2-x(m+n)+mn = 0
The graph of a quadratic equation is a parabola
A quadratic equation can be solved by the graphical method also
PROBLEMS SOLVING : PROBLEMS SOLVING 1)SOVE THE EQUATION
X?2/2 - 3/4 = 7 ΒΌ
2)X 2 +15X +50 = 0
QUADRTIC EQUATIONS-SUMS : QUADRTIC EQUATIONS-SUMS 3) 13m = 6(m2 + 1 )
QUADRATIC EQUATIONS- SUMS : QUADRATIC EQUATIONS- SUMS 4) 0.2x2 - 0.04x = 0.03
QUADRATIC EQUATIONS : QUADRATIC EQUATIONS 5) Find the value of p for which (p-2)(p-3) + (p-4)(p-5) = 0
QUADRATIC EQUATIONS : QUADRATIC EQUATIONS 6) If m and n are the roots of the equation 2x2-6x+1 =0, find the value of
a) m2n +mn2 b) m2 + n2
QUADRATIC EQUATIONS : QUADRATIC EQUATIONS 7)Form the quadratic equation whose roots are squares of the roots of the equation x2 +2x+5 =0
QUADRATIC EQUATIONS : QUADRATIC EQUATIONS 8)If the sums of squares of two successive even number is 100, find the numbers
QUADRATIC EQUATIONS : QUADRATIC EQUATIONS 9) Draw a graph of x2 -x + 11 = 0, What is the nature of its roots
QUADRATIC EQUATIONS : QUADRATIC EQUATIONS 10)Solve the quadratic equation 2x2 -3x -5 = 0 graphically.
CONCLUSION : CONCLUSION All the ten problems given are solved during the online class.
In case of any doubts or clarification noticed by a student subsequently, he is welcome to contact me through email any time for assistance
Students are welcome to bring to my notice any specific problem which could not be tackled in any subsequent class for solving depending upon the time availability. Other wise solution will be explained to the student in detail by mail.
Students are advised to feel free if they are not able to assimilate any topic to their satisfaction by bringing to me notice.
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manjulab64@gmail.com