1How can the value of \( x \) in the quadratic equation \( ax^2 + bx + c = 0 \) be found?
2Solve by using the formula: \( x^2 - 5x + 6 = 0 \)
3Solve by using the formula: \( x\left(x - \frac{2}{7}\right) = \frac{3}{49} \)
4Is \( (x - 2)^2 + 1 = 2x - 3 \) a quadratic equation? Give a reason.
5Is \( x(x + 1) + 8 = (x + 2)(x - 2) \) a quadratic equation? Give a reason.
6Is \( x(2x + 3) = x^2 + 1 \) a quadratic equation? Give a reason.
7Is \( (x + 2)^3 = x^3 - 4 \) a quadratic equation? Give a reason.
8Is \( x^2 + 3x + 1 = (x - 2)^2 \) a quadratic equation? Give a reason.
9Is \( (x + 2)^3 = 2x(x^2 - 1) \) a quadratic equation? Give a reason.
10Solve by factorisation: \( x^2 - 3x - 10 = 0 \)
11Solve by factorisation: \( 2x^2 + x - 6 = 0 \)
12Solve by factorisation: \( 2x^2 - x + \frac{1}{8} = 0 \)
13Solve by factorisation: \( 100x^2 - 20x + 1 = 0 \)
14Solve by factorisation: \( x^2 - 45x + 324 = 0 \)
15Solve by factorisation: \( x^2 - 27x - 182 = 0 \)
16Solve by completing the square: \( x^2 - 6x + 9 = 0 \)
17Solve by completing the square: \( 9x^2 - 15x + 6 = 0 \)
18Solve by completing the square: \( 2x^2 - 5x + 3 = 0 \)
19Solve by completing the square: \( 5x^2 - 6x - 2 = 0 \)
20Solve by completing the square: \( x^2 + \frac{15}{16} = 2x \)
21Solve by completing the square: \( x^2 + \frac{2}{3}x = \frac{35}{9} \)
22Solve by using the formula: \( x^2 - 9x + 20 = 0 \)
23Solve by using the formula: \( x^2 + 2x - 143 = 0 \)
24Solve by using the formula: \( 3x^2 - 5x + 2 = 0 \)
25Solve by using the formula: \( 2x^2 - 2\sqrt{2}\,x + 1 = 0 \)
26Solve by using the formula: \( x + \frac{1}{x} = 3 \)
27Solve by using the formula: \( \frac{1}{x} + \frac{1}{x - 2} = 3 \)
28Solve by using the formula: \( \frac{1}{x + 4} - \frac{1}{x - 7} = \frac{11}{30} \)
29Ramnaresh Mahato scored a total of 30 marks in two subjects, English and Mathematics, in the first terminal examination of grade 10. If he had scored 2 more marks in Mathematics and 3 fewer marks in English, the product of his marks would have been 210. Find his scores in both subjects.
30The longer side of a rectangular playground is 30 m more than its shorter side, and its diagonal is 60 m more than its shorter side. Find the length and breadth of the playground.
31Artificial grass turfs of size 12 m × 3 m are to be laid on the playground, which is 120 m long and 90 m broad. How many turfs are needed?
32The playground, 120 m long and 90 m broad, is to be fenced 4 times round with barbed wire costing Rs. 15 per metre. How much will it cost?
33Why does the quadratic formula contain the sign \( \pm \)?
34Why must \( a \neq 0 \) when the quadratic formula is used?
35Solve by using the formula: \( 2x^2 + 7x + 3 = 0 \)
36The product of two consecutive positive integers is 132. Find the integers.