Find the roots of the following quadratic equations (if they exist) by the method of completing the square. 3x²+11x+10=0
Answers
SOLUTION :
Given : 3x² + 11x + 10 = 0
On dividing the whole equation by 3,
(x² + 11x/3 + 10/3) = 0
Shift the constant term on RHS
x² + 11x/3 = - 10/3
Add square of the ½ of the coefficient of x on both sides
On adding (½ of 11/3)² = (11/6)² both sides
x² + 11x/3 + (11/6)² = - 10/3 + (11/6)²
Write the LHS in the form of perfect square
(x + 11/6)² = - 10/3 + 121/36
[a² + 2ab + b² = (a + b)²]
(x + 11/6)² = (-10 × 12 + 121)/36
(x + 11/6)² = (-120 + 121)/16
(x + 11/6)² = 1/36
On taking square root on both sides
(x + 11/6) = √(1/36)
(x + 11/6) = ± 1/6
On shifting constant term (11/6) to RHS
x = ± 1/6 - 11/6
x = 1/6 - 11/6
[Taking +ve sign]
x = (1 - 11)/6
x = - 10/6
x = - 5/3
x = - 1/6 - 11/6
[Taking - ve sign]
x = ( - 1 - 11)/6
x = - 12/6
x = - 2
Hence, the roots of the given equation are - 2 & - 5/3.
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HENCE SOLVED
ANSWERED BY ARJUN
