Quadratic Formula


 
 
Concept Explanation
 

Quadratic Formula

The Quadratic Formula: For a quadratic equation

large ax^2+bx+c = 0, ;where; aneq 0

Using Completing the square method we can find the roots

large ax^2+bx=-c

large x^2+frac{b}{a}x=-frac{c}{a}

large x^2+2left ( frac{b}{2a} right )x + left (frac{b}{2a} right )^2=-frac{c}{a}+ left (frac{b}{2a} right )^2

large left (x+ frac{b}{2a} right )^2=-frac{c}{a}+ left (frac{b^2}{4a^2} right )

large left (x+ frac{b}{2a} right )^2=left(frac{b^2-4ac}{4a^2} right )

large left (x+ frac{b}{2a} right )=pm left (frac{sqrt{b^2-4ac}}{2a} right )

large x=- frac{b}{2a} pm left (frac{sqrt{b^2-4ac}}{2a} right )

large x=frac{-bpm sqrt{b^2-4ac}}{2a}

large x=frac{-bpm sqrt{D}}{2a}, ;where; D=b^2-4ac

Example: Find the solution of quadratic equation:

large -3x^2+5x-2=0

Solution: Comparing with standard form we get

a= -3, b= 5 and c= -2

large D= b^2-4ac= (5)^2-4 X (-3) X (-2)= 25-24=1

So the solutions are

large x=frac{-(5)pm sqrt{1}}{2(-3)}

large x=frac{-5pm 1}{-6}

 large Either;x=frac{-5-1}{-6}; or; x=frac{-5+1}{-6}

large Either;x= 1; or; x=frac{2}{3}

Sample Questions
(More Questions for each concept available in Login)
Question : 1

Find the value of the discriminant for the quadratic equation

frac{2}{7}x^2+5x+42=0

Right Option : B
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Explanation
Question : 2

Find the value of sqrt{{a+}sqrt{a+sqrt{a+}}}----------varpi

Right Option : C
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Explanation
Question : 3

Find the value of discriminant for the equation  x^2+5x+6=0

Right Option : C
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Explanation
 
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