F ( x ) = 0 F(x)=0 F ( x ) = 0
F ( x ) = 8 x 2 + 3 x − 6 = 0 F(x)=8x^2+3x-6=0 F ( x ) = 8 x 2 + 3 x − 6 = 0
Now we can not find its root by normal factorization method;so we use here Shree Dharacharya Formula.
For this compare the equation 8 x 2 + 3 x − 6 8x^2+3x-6 8 x 2 + 3 x − 6 = 0 =0 = 0 by a x 2 + b x + c = 0 ax^2+bx+c=0 a x 2 + b x + c = 0
From above comparison we have
a = 8 , b = 3 , c = − 6 a=8,b=3,c=-6 a = 8 , b = 3 , c = − 6
Hence root = = =
x = − b ± b 2 − 4 a c 2 a x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a} x = 2 a − b ± b 2 − 4 a c
Putting the values of a,b,c in the above equation.
x = − 3 ± ( − 3 ) 2 − 4 ( 8 ) ( − 6 ) 2 × 8 x=\frac{-3\pm \sqrt{(-3)^2-4(8)(-6)}}{2\times8} x = 2 × 8 − 3 ± ( − 3 ) 2 − 4 ( 8 ) ( − 6 )
x = − 3 ± 9 + 192 16 x=\dfrac{-3\pm\sqrt{9+192}}{16} x = 16 − 3 ± 9 + 192
x = − 3 ± 201 16 x=\dfrac{-3\pm\sqrt{201}}{16} x = 16 − 3 ± 201
x = − 3 ± 13.85 16 x=\dfrac{-3\pm13.85}{16} x = 16 − 3 ± 13.85
x = − 3 + 13.85 16 , − 3 − 13.85 16 x=\dfrac{-3+13.85}{16},\dfrac{-3-13.85}{16} x = 16 − 3 + 13.85 , 16 − 3 − 13.85
x = 0.68 , − 1.05 x=0.68,-1.05 x = 0.68 , − 1.05
So the two roots of the equation are 0.68 , − 1.05 0.68,-1.05 0.68 , − 1.05 .
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