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Quadractic Formula

Theory & Practice Question.

Theory

 
Quadractic formula

When a quadractic equation of the form ax² + bx + c = 0 cannot be
factorised, the quadractic formula can be used to solve for x :

x=(-b±√(b^2-4ac))2a,a ≠ 0

Note: If b² - 4ac < 0 there is no solution.

 

Example

Solve the following equation for  using the quadratic formula:

+3x-5=0

 

Solution

Recall the quadratic formula for the quadratic ax² + bx + c = 0 

x=(-b±√(b^2-4ac))2a,a ≠ 0

Therefore:

+3x-5=0

a=1 b=3 c=-5

Substituting values:

x=(-3±√(3^2-(41-5)))2

x=(-3±√(9+20))2

x=(-3+√29)2 or x=(-3-√29)2

 

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