Question

14. Find the roots of 3x - 5x + 2 = 0 by the method of completing the square.​

Answer 1

Answer:-

Equation : 3x² - 5x + 2 = 0

Step 1 : Make first term 1x².

3x²/3 - 5x/3 + 2/3 = 0

x² - 5x/3 + 2/3 = 0

Step 2 : Shift constant term.

x² - 5x/3 = -2/3

Step 3 : Add (b/2)² on both sides.

x² - 5x/3 + 25/36 = -2/3 + 25/36

(x - 5/6)² = (-72+75)/108

(x - 5/6)² = 3/108

(x - 5/6)² = 1/36

x - 5/6 = √(1/36)

x - 5/6 = ±1/6

So, either x - 5/6 = +1/6 or x - 5/6 = -1/6

Hence, x = 1/6 + 5/6 or x = -1/6 + 5/6

So, x = 1 or x = 2/3

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Three methods of solving the quadratic equation include:-

• Completing the square method
• Splitting the middle term
• Quadratic equation/Shreedhara charya Formula

Answer 2

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$\huge\tt{TO~SOLVE:}$

• Find the roots of 3x - 5x + 2 = 0
• By the method of completing the square.

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$\huge\tt{SOLUTION:}$

➩3x² - 5x + 2 = 0

➩3x²/3 - 5x/3 + 2/3 = 0

➩x² - 5x/3 + 2/3 = 0

➩x² - 5x/3 = -2/3

➩x² - 5x/3 + 25/36 = -2/3 + 25/36

➩(x - 5/6)² = (-72+75)/108

➩(x - 5/6)² = 3/108

➩(x - 5/6)² = 1/36

➩x - 5/6 = √(1/36)

➩x - 5/6 = ±1/6

➩x - 5/6 = +1/6 or x - 5/6 = -1/6

➩x = 1/6 + 5/6 or x = -1/6 + 5/6

➩x = 1 or ⅔

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