2.2c Solving Quadratic Equations – Quadratic Formula

The quadratic equation \(a{x^2} + bx + c = 0\) can be solved by using the quadratic formula
b± b 2 4ac 2a
Example 
Use the quadratic formula to find the solutions of the following equations.
a. \({x^{\rm{2}}} + {\rm{ 5}}x-{\rm{ 24 }} = {\rm{ }}0\)
b. \(x\left( {x + {\rm{ 4}}} \right){\rm{ }} = {\rm{ 10}}\)
Answer
a. For the equation \({x^{\rm{2}}} + {\rm{ 5}}x-{\rm{ 24 }} = {\rm{ }}0\)
a = 1, b = 5, c = -24
x= b± b 2 4ac 2a x= (5)± (5) 2 4(1)(24) 2(1) x= 5± 121 2 x=8 or x=3
b.
x( x+ 4 ) = 10 x 2 +4x10=0 a=1,  b=4,  c=10 x= b± b 2 4ac 2a x= (4)± (4) 2 4(1)(10) 2(1) x= 4± 56 2 x=1.742 or x=5.742

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