Roots of quadratic equation formula

Roots of quadratic equation formula

 we know that  ax²+bx+c=0

then  ax²+2(b/2a)x+(b/2a)²-(b/2a)²+c=0

⇒ (x+b/2a)²=(b/2a)²-c

⇒x+b/2a= ±√((b/2a)²-c)

⇒x=-b/2a±{√((b)²-4ac)}/2a

x={-b±√((b)²-4ac)}/2a

hense,  the Roots of quadratic equation formula
x = {−b + √(b² − 4ac)}/ 2a
 x = {−b -√(b² − 4ac)}/ 2a 

Q.the sum of the roots of the quadratic equation 3x²-9x+5 =0 is

solution:-Given 3x²-9x+5 =0 

here,a=3 ,b=-9 ,c=5

the Roots of quadratic equation 

{-b±√(b^2-4ac)}/2a

Put 

⇒x=[-(-9) ± √{(-9)^2-4×3×5}]/2×5

⇒x=[9 ± √{81-60}]/10

⇒x=[9 ± √21]/10

If take first + sign then

⇒x=[9 + √21]/10
If take - sign then 
⇒x=[9 -√21]/10
hense,  the Roots of quadratic equation x={9+ √21}/6,{9- √21}/6

Q.The sum of the roots of the quadratic equation 3x²-2√6x+2=0 is

solution:- given equation 3x²-2√6x+2=0

                 here a=3 ,b=-2√6, c=2

the Roots of quadratic equation 

{-b±√(b^2-4ac)}/2a

Put 

⇒x=[-(-2√6) ± √{(-2√6)^2-4×3×2}]/2×3

⇒x=[2√6 ± √{24-24}]/6

⇒x=[2√6± 0]/6

If take first + sign then

⇒x=[2√6 + 0]/6

 x=2√6/6

x=√6/3
If take - sign then 
⇒x=[2√6- 0]/6

x=2√6/6

x=√6/3
hense,  the Roots of quadratic equation are equal √6/3 , √6/3

find the roots of the quadratic equation 3x2-2√6x+2=0

solve x^2-6x+2=0 by completing the square

6x²-x-2=0

solve the following quadratic equations for x: 4 3x 2 + 5x − 2 3 = 0

the sum of the roots of the quadratic equation 3x^2-9x+5=0 is

,

x^2-6x-2=0 quadratic formula

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