Second Degree Equations — Practice Quiz
Kerala Board · Class 10 · Mathematics
Try a 4-question quiz on Second Degree Equations for Kerala Board Class 10 Mathematics: tap an answer to check it and see why.
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Quick Quiz: Second Degree Equations
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When a square was enlarged by extending each side by 3 metres, its area became 100 square metres. What was the length of a side of the original square?
Complete the square for the expression x² + 8x. What number should be added?
One side of a rectangle is 4 metres longer than the other and its area is 60 square metres. What are the lengths of the sides?
The product of two consecutive even numbers is 168. What are the numbers?
Sample Questions
Solve the equation (x - 5)² = 36. What are the possible values of x?
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x = 11, x = -1
From (x - 5)² = 36, we get x - 5 = ±6. So x - 5 = 6 gives x = 11, and x - 5 = -6 gives x = -1. Both solutions are valid algebraically.
Which of the following expressions can be written as perfect squares?
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x² + 6x + 9, x² - 10x + 25, x² - 8x + 16
x² + 6x + 9 = (x+3)², x² - 10x + 25 = (x-5)², x² - 8x + 16 = (x-4)². But x² + 4x + 5 cannot be written as a perfect square since 4² ≠ 4×4 = 16 ≠ 5×4 = 20.
A right triangle has perpendicular sides where one is 3 cm more than the other. If the area is 35 cm², what are the lengths of these sides?
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7 cm and 10 cm
Let the shorter side be x cm, longer side = (x+3) cm. Area = ½x(x+3) = 35, so x(x+3) = 70. This gives x² + 3x = 70. Completing square: x² + 3x + 9/4 = 70 + 9/4 = 289/4. So (x + 3/2)² = 289/4, x + 3/2 = 17/2, x = 7. Sides are 7 cm and 10 cm.
If x² - 12x + 36 = 0, what is the value of x?
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6
Notice that x² - 12x + 36 = (x-6)². So the equation becomes (x-6)² = 0, which means x-6 = 0, therefore x = 6. This is a perfect square trinomial with only one solution.
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Sources & Official References
- Kerala Board of Public Examinations — keralapareekshabhavan.in
- National Education Policy 2020 — education.gov.in
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