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# Quadratic equation

this is a quite simple but nice ppt on quadratic equations submitted by me as my project

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### Quadratic equation

1. 1. I Would Really Like To Thank Farooq Sir For Giving Such A WonderfulProject To Work On. It Has Not Only Been A Pleasure But Also AWonderful Experience Working On This Project. I Would Like To ExtendMy Gratitude To All The People Those Who Helped As Well As MotivatedMe To Make This Project. THANKYOU ALL NIKHIL RAVI AND TEAM
2. 2. Definition:A quadratic function is a function of theform f ( x)  ax  bx  c 2where a, b, c are real numbers and a 0.The expression on the right-hand-side ax  bx  c 2 is call a quadratic expression.
3. 3. A quadratic function is any equation with adegree* of two.A quadratic equation is a trinomial** expressionbecause in standard form it adds three terms(ax², bx, and c).*Degree: The highest power of any term of apolynomial (Algebra to Go).**Trinomial: A polynomial (the sum of terms) withthree terms (the product of constants and variables)
4. 4. The numbers that satisfy the equation are calledsolutions or roots.The various methods of solving quadraticequations is :-• Factorization• Using the Quadratic Formula
5. 5. Method 1: FactorizationQ. Factorize ax  bx  c 2If ax  bx  c  (rx  p)( sx  q) 2then the solutions (roots) of theequation are p q x1   and x2   r s
6. 6. x  2 x  15  0 2( x  5)( x  3)  0x  5, x  32x  7x  3  0 2(2 x  1)( x  3)  0 1x  3, x  2
7. 7. METHOD 2: USE THE QUADRATIC FORMULAThe quadratic formula is often written as b  b  4ac 2 x 2a The number b2  4ac is called the discriminant.
8. 8. Given the quadratic equation ax  bx  c  0. 2 If :-b  4ac  0, 2 the equation has real, unequal rootsb  4ac  0, 2 the equation has real, equal rootsb  4ac  0, 2 the equation has complex roots
9. 9. 2x  7x  3  0 2 (7)  (7)  4(2)(3) 2x 2(2) 7  49  24 7  25 7  5    4 4 4 75 75 1x1   3, x2   4 4 2
10. 10. x 2  3x  5  0 3  32  4(1)(5)x 2(1) 3  29  2 3  29 3  29x1  , x2  2 2
11. 11. This Project Was Fruitful For Me. I Have Learnt A Lot Of Things Which WillBenefit Us And Also Help Us In The Future . A Lot Of Things About QuadraticsHas Been Discussed In The Project . The Definition , Types , Ways Of SolvingAs Well As Solved Examples . We Surely Hope That You Will Like The Project.