Quadratic Equation

Quadratic Equation | Class 10

Mathematics Question for revision

There will be 10 questions and timing will be 1 hour.

1. Find the roots of the following quadratic equations by factorisation:
i) 100x² – 20x + 1 = 0
ii) 2x² + x – 6 = 0
iii) 2x² – x +1/8 = 0

2. Find the roots of the following quadratic equations, if they exist, by the method of completing the square:
(i) 2x² – 7x +3 = 0
(ii) 2x² + x – 4 = 0
(iii) 4x² + 4√3x + 3 = 0

3. Find the roots of the following equations:
(i) x-1/x = 3, x ≠ 0
(ii) 1/x+4 – 1/x-7 = 11/30, x ≠ -4, 7

4. Prove the quadratic formula for finding the roots using the completing the square method

5.Find the nature of the roots of the following quadratic equations. If the real roots exist, find them.
i) 2x² – 3x + 5 = 0
(ii) 3x² – 4√3x + 4 = 0
(iii) 2x² – 6x + 3 = 0

6. Find the values of k for each of the following quadratic equations so that they have two equal roots.
(i) 2x² + kx + 3 = 0
(ii) kx (x – 2) + 6 = 0

7. The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.

8.In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.

9. The sum of the reciprocals of Rehman’s age (in years) 3 years ago and 5 years from now is 1/3. Find his present age.

10.The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.

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