1. To complete the square for x² + 6x, what constant must be added?
- A3
- B6
- C9
- D12
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Answer: C) 9
Add (half of 6)² = 3² = 9. Then x² + 6x + 9 = (x + 3)².
Class 10 Completing the Square — practice questions with answers
Quadratic Equations · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
2. For 2x² + 8x + 6 = 0, the first step in completing the square is to:
- ADivide the whole equation by 2
- BAdd 6 to both sides
- CMultiply by 2
- DSquare the constant term
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Answer: A) Divide the whole equation by 2
Make the leading coefficient 1 first: divide by 2 to get x² + 4x + 3 = 0.
3. For 4x² + 4x + 1 = 0, completing the square gives (2x + 1)² = 0. The root is:
- A
- B
- C-1
- D
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Answer: A)
(2x + 1)² = 0 gives 2x + 1 = 0, so x = (repeated root).
4. Using p35-style logic, the roots of x² + 5x - 14 = 0 (from (x + )² = ) are:
- A2 and -7
- B-2 and 7
- C2 and 7
- D-2 and -7
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Answer: A) 2 and -7
x + = +/-, so x = - = 2 or x = - = -7.
5. A two-digit number is such that the product of its digits is 18.
When 63 is added to the number, the digits interchange. The tens digit x satisfies x² - 9x + 18 = 0 in the related setup.
Solve x² - 9x + 18 = 0 by completing the square; the roots are:
When 63 is added to the number, the digits interchange. The tens digit x satisfies x² - 9x + 18 = 0 in the related setup.
Solve x² - 9x + 18 = 0 by completing the square; the roots are:
- A3 and 6
- B2 and 9
- C1 and 18
- D-3 and -6
Show answer
Answer: A) 3 and 6
x² - 9x = -18, add : (x - )² = - 18 = , x - = +/-, x = 6 or x = 3.
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