The constant term in the polynomial P(x) is the term that does not contain any variable, which is -7.

The discriminant is zero, indicating that the roots are real and equal.

The discriminant is 0 (b² - 4ac = 0), indicating that the roots are real and equal.

The differences are 3, 5, 7, which are increasing by 2 each time.

The pattern is to add consecutive odd numbers: 2 + 3 = 5, 5 + 5 = 10, 10 + 7 = 17. The next term is 17 + 9 = 26.

Using the property that the sum of angles in a triangle is 180 degrees, angle C can be calculated as 180 - (30 + 60) = 90 degrees.

Since two angles are equal (45 degrees each), triangle DEF is an isosceles triangle.

Since all sides are of different lengths, triangle XYZ is a scalene triangle.

Since all sides are of different lengths, triangle XYZ is a scalene triangle.

The longest side in triangle XYZ is XZ, which measures 10 cm.

Let the ages be 4x and 5x. Then, 4x + 5x = 72, leading to 9x = 72, so x = 8. The older sibling's age is 5x = 40.

Area = base × height. Thus, 120 = 15 × height, giving height = 120/15 = 8 m.

Area = base × height. Thus, 120 = 15 × height, giving height = 120/15 = 8 units.

Area = (1/2) × d1 × d2. Thus, 48 = (1/2) × 8 × d2, giving d2 = 12 cm.

Area = (1/2) × d1 × d2. Thus, 60 = (1/2) × 10 × d2, giving d2 = 12 cm.

Area = (1/2) × d1 × d2. Thus, 60 = (1/2) × 10 × d2, giving d2 = 60/(5) = 12 cm.

The author implies that a collective effort is necessary to effectively address the complex issue of inequalities.

The phrase 'the cycle of poverty' highlights how different forms of inequality are interconnected and perpetuate each other.

Let the number of items be n. Total sum = 50n. After removing one number, the new sum = 48(n - 1). Setting up the equation gives the removed number as 52.

Let the integers be x, x+1, x+2. The average is (x + (x + 1) + (x + 2)) / 3 = 20. Solving gives x = 18.

New average = (72 * 5 + 80) / 6 = (360 + 80) / 6 = 440 / 6 = 73.33, which rounds to 74.

The pair 5 and 12 has an HCF of 1 and an LCM of 60.

Using the relation HCF * LCM = Product of the numbers, we have 7 * 84 = 21 * x, which gives x = 42.

Using the relation HCF * LCM = Product of the numbers, we have 8 * 120 = 32 * x, which gives x = 40.

Using the relation: LCM * HCF = Product of the numbers, we have 84 * 12 = 36 * x, solving gives x = 28.

Let the two numbers be 12x and 12y. Then, LCM(12x, 12y) = 12 * LCM(x, y) = 84, which gives LCM(x, y) = 7. The pairs (x, y) that satisfy this are (3, 4) or (4, 3), leading to 24 and 42.

The sum of the first n terms of a harmonic progression can be expressed as 2n/(a+b) where a and b are the first two terms.

Using the relationship between HCF, LCM, and the numbers: (21 * x) / 7 = 84. Solving gives x = 42.

Using the relationship LCM = (Product of the numbers) / HCF, we can find the other number: 72 = (16 * x) / 8, leading to x = 24.

The domain of a function refers to the set of all possible input values (x-values) for which the function is defined.