Finding roots of quadratic equation using completing square method.
Find the roots of the equation 5x²-6x-2=0 by completing the square.
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Finding roots of quadratic equation using completing square method.
Sidharth
The roots of the given equation =>(3±√19 )/5
Given equation=> 5x^2 -6x -2=0
Making the coefficient of x^2 to 1: x^2 -6/5 x – 2/5 =0
=> x^2 -2*(3/5)x=2/5 ——(1)
Convert the equation 1 inro (a-b)^2 form
In LHS side there is x^2 -2*(3/5)x => a^2 -2ab +b^2
Here a=x , b=3/5. So, add (3/5)^2 on both sides of equation 1
x^2 -2*(3/5)x +(3/5)^2 = 2/5+(3/5)^2
(x-3/5)^2 = 19/25
x-3/5 = ±√19 /5
x=(3±√19 )/5
∴ The roots of the given equation are (3+√19 )/5 and (3-√19 )/5
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if x=acostheta+bsintheta and y=asintheta-bcostheta then prove that y 2 d 2y/dx^2 xdy/dx + y = 0