Question

solve quadratic equation 3x^2+√21x- 14=0, by completing square method

Answer 1

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Answer 2

Given:

Quadratic equation 3x^2+√21x- 14=0

To Find:

Solve the quadratic equation by completing the square method

Solution:

A quadratic equation is a polynomial equation with a degree equal to two. A quadratic equation is written as follows:

ax² + bx + c = 0, where a, b, and c are real values, a is not equal to zero, and x is a variable.

It can be solved by various methods one of them is completing the square method.

''Completing the square method: we have to convert the given equation into a perfect square.''

According to the question:

3x²+√21x- 14=0

Dividing by 3 to make the coefficient of x² = 1.

3x²/3 + (√21/3)x - 14/3 = 0

x² + (√21/3)x - 14/3 = 0

[ Adding and subtracting the square of half of (√21/3) i.e (1/2)x(√21/3) ]

x² + (√21/3)x + (√21/6)²  - (√21/6)² - 14/3 = 0

Now,

(a+b)² = a² + b² +2ab

Here,

a = x

b = √21/6

So,

(x + √21/6)² -  (√21/6)² - 14/3 =0

(x + √21/6)² =  (√21/6)² + 14/3  

(x + √21/6)² = 21/36 + 14/3     [Taking L.C.M ]

(x + √21/6)² = 189/36  

√(x + √21/6)² = √189/36    [ Taking square root both side]

(x + √21/6) = ± 3√21/6        [∵√189 = √(3×3×21)]

x = - √21/6 ± √21/2

So,

x1 =  - √21/6 + √21/2

   = (-√21 + 3√21)/6

   =2√21/6

   = √21/3

x2 =  - √21/6 -√21/2

    =   (-√21 - 3√21)/6

   = -4√21/6

   =( -2√21)/3

Hence, the roots of the quadratic equation 3x²+√21x- 14=0, by completing the square method are  √21/3 and (-2√21)/3