SOLVING QUADRATIC EQUATION : Solving by Quadratic Formula
Apart from factoring method, quadratic equation can be solved by quadratic formula and given as below,
x=−b±√b2−4ac2a
How to - Solving Quadratics Equation : Solving by Quadratic Formula?
To solve a quadratic equation by quadratic formula.
- Transform the equation into standard form.
- Obtain the values of a, b and c from given equation.
- Substitute the three values into quadratic formula.
- Calculate the two values of x
a)x2+6x+5=0a=1, b=6, c=5x=−b±√b2−4ac2ax=−(6)±√(6)2−4(1)(5)2(1)x=−6±√162x=−6±42so,x=−6+42, x=−6−42x=−1, x=−5¯¯
b) x2+10x+9=0a=1, b=10, c=9x=−b±√b2−4ac2a=−(10)±√(10)2−4(1)(9)2(1)=−10±√642=−10±82x=−10+82, x=−10−82 x=−1, x=−9¯¯
c) x(x+3)=40x2+3x=40x2+3x−40=0x=−b±√b2−4ac2ax=−(3)±√(3)2−4(1)(−40)2(1)x=−3±√1692x=−3±132x=−3+132, x=−3−132x=5, x=−8¯¯
Here are three examples: Bear in mind that positive and negative sign of the roots play important role in this method.
Try it yourself - Solving Quadratic Equation : Solving quadratic equation by using Quadratic formula
a) x2−7x=−10b) 2x2=3xc)x(x−8)=2x−25}ans-x=2,5ans-x=0,32ans-x=5
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