Page 1 Quadratic Equations Page 2 Quadratic Equations Quadratic Equations Factorization Method Completing The Square Method An equation of the form ax 2 + bx + c = 0, where a, b & c are real numbers & a = 0 is known as a Quadratic Equation A Polynomial of degree 2 is known as a Quadratic Polynomial Quadratic Formula Method ax 2 + bx + c = 0 ax 2 + bx + c = 0 ax 2 + bx + c = 0 Multiply a & c a x c = h Find two numbers whose product is h and sum is b These two numbers can be a and b or any other (p, q) Split the middle term accordingly & take out the common factors Finally we’ll get a product of two linear equations & hence we can get two values of x i.e. roots of the equation Divide the entire equation by a Take the constant c / a on R. H. S. Now add ( x coecient of x) 2 on both the sides (L.H.S. & R.H.S.) So L.H.S. can be written as where b is the coecient of x Now take square root on both the sides & then simplify the linear equation to get roots of x Step 1 : Step 2 : Step 3 : Step 4 : Step 5 : Step 1 : Step 2 : Step 4 : Step 3 : Step 5 : 1 2 Simply take a, b & c with their respective sign Find the two roots of the equation or Step 1 : Step 2 : Step 3 : -b ± b 2 - 4ac x = 2a -b + b 2 - 4ac x = 2a -b - b 2 - 4ac x = 2a ) 2 (x + b 2a QUADRATIC EQUATIONS 10 Page 3 Quadratic Equations Quadratic Equations Factorization Method Completing The Square Method An equation of the form ax 2 + bx + c = 0, where a, b & c are real numbers & a = 0 is known as a Quadratic Equation A Polynomial of degree 2 is known as a Quadratic Polynomial Quadratic Formula Method ax 2 + bx + c = 0 ax 2 + bx + c = 0 ax 2 + bx + c = 0 Multiply a & c a x c = h Find two numbers whose product is h and sum is b These two numbers can be a and b or any other (p, q) Split the middle term accordingly & take out the common factors Finally we’ll get a product of two linear equations & hence we can get two values of x i.e. roots of the equation Divide the entire equation by a Take the constant c / a on R. H. S. Now add ( x coecient of x) 2 on both the sides (L.H.S. & R.H.S.) So L.H.S. can be written as where b is the coecient of x Now take square root on both the sides & then simplify the linear equation to get roots of x Step 1 : Step 2 : Step 3 : Step 4 : Step 5 : Step 1 : Step 2 : Step 4 : Step 3 : Step 5 : 1 2 Simply take a, b & c with their respective sign Find the two roots of the equation or Step 1 : Step 2 : Step 3 : -b ± b 2 - 4ac x = 2a -b + b 2 - 4ac x = 2a -b - b 2 - 4ac x = 2a ) 2 (x + b 2a QUADRATIC EQUATIONS 10 Nature of Roots: D = b 2 - 4ac D iscriminant is known for discriminating real and non-real roots as well as to dene nature of roots. Conditions: When D = 0, roots are real & equal When D > 0, roots are real & unequal When D < 0, roots are non-real & unequal Introduction of Quadratic equation and Factorization method Scan the QR Codes to watch our free videos Quadratic formula is derived from completing the square method In word questions, try to nd words like product, area, Pythagoras theorem, etc; where we will multiply two terms to obtain a quadratic equation. In word problem, the solution thus obtained should always be checked with conditions given in the question. PLEASE KEEP IN MIND Speed = , please remember this formula. A variety of questions on quadratic equations are based on the concept of speed. Also do remember conversions like 1 hour = 60 minutes, 1 minute = 60 seconds. ? To determine whether an equation is quadratic or not, expand the given equation, simplify it as much as possible and then check the highest degree. ? ? ? ? Distance Time QUADRATIC EQUATIONS 11Read More

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