find x : 8x2+3x-6=0
"F(x)=0"
"F(x)=8x^2+3x-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 "8x^2+3x-6" "=0" by "ax^2+bx+c=0"
From above comparison we have
"a=8,b=3,c=-6"
Hence root "="
"x=\\dfrac{-b\\pm \\sqrt{b^2-4ac}}{2a}"
Putting the values of a,b,c in the above equation.
"x=\\frac{-3\\pm \\sqrt{(-3)^2-4(8)(-6)}}{2\\times8}"
"x=\\dfrac{-3\\pm\\sqrt{9+192}}{16}"
"x=\\dfrac{-3\\pm\\sqrt{201}}{16}"
"x=\\dfrac{-3\\pm13.85}{16}"
"x=\\dfrac{-3+13.85}{16},\\dfrac{-3-13.85}{16}"
"x=0.68,-1.05"
So the two roots of the equation are "0.68,-1.05" .
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