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

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- 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. 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. 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. The numbers that satisfy the equation are calledsolutions or roots.The various methods of solving quadraticequations is :-• Factorization• Using the Quadratic Formula
- 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. 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. 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. 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. 2x 7x 3 0 2 (7) (7) 4(2)(3) 2x 2(2) 7 49 24 7 25 7 5 4 4 4 75 75 1x1 3, x2 4 4 2
- 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. 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.

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