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