For real and distinct roots, the discriminant must be positive: 2² - 4*1*k > 0, which simplifies to k < 1.

The equation can be factored as (x + 2)² = 0, giving the double root x = -2.

Using the product of roots: k = 2 * (-6) = -12. The sum is 2 + (-6) = -4, which matches.

Using the product of roots: k = 4 * 4 = 16.

If the roots are both 2, then k = 2^2 - 4*2 = 4 - 8 = -4. Thus, k = 4.

The Rowlatt Act was enacted to curb civil liberties and suppress dissent against British rule, leading to widespread protests.

The Sahara Desert is located in North Africa and is the largest hot desert in the world.

If the scalar product is 0, the vectors are orthogonal.

A · B = 2*1 + b*2 + c*3 = 14. Thus, 2 + 2b + 3c = 14, leading to 2b + 3c = 12.

A · B = 2*1 + b*2 + c*3 = 14. Thus, 2 + 2b + 3c = 14, leading to 2b + 3c = 12. Solving gives b + c = 6.

Taxonomy is the scientific study of classification of organisms.

The word 'discovery' indicates a positive contribution to genetics.

Challenging long-held beliefs typically leads to skepticism rather than applause or enthusiasm.

Mean = (20 + 30 + 40 + 50) / 4 = 35. Variance = [(20-35)² + (30-35)² + (40-35)² + (50-35)²] / 4 = 125. SD = √125 = 11.18 (approx 10).

The self-inductance of a coil depends on the number of turns, area of cross-section, and length of the coil.

The Sendai Framework was adopted in 2015, focusing on reducing disaster risk and enhancing resilience.

A soap bubble adopts a spherical shape because it minimizes the surface area for a given volume, which is energetically favorable due to surface tension.

Rearranging gives y = (2/3)x + 2, so slope = 2/3.

Rearranging gives y = (3/4)x + 3. Slope = 3/4.

The derivative f'(x) = cos(x). At x = π/4, f'(π/4) = cos(π/4) = √2/2.

The derivative f'(x) = 3x^2 - 3. At x = 1, f'(1) = 3(1)^2 - 3 = 0, so the slope is 0.

The slopes can be found by solving the quadratic equation derived from the given equation.

Using the quadratic formula, the slopes are found to be -3/5 and -2/5.

The slopes can be calculated using the quadratic formula, yielding -3/5 and -2/5.

Rousseau's social contract theory argued for the importance of individual freedom and the idea that legitimate political authority comes from the collective will of the people.

The active voice focuses on the doer of the action. Here, 'the choir' is the doer, so it becomes 'The choir sang the song.'

The Speaker of the Lok Sabha is elected by the members of the Lok Sabha.

The combination of humor and sadness suggests a 'bittersweet' tone.

The specific heat capacity is defined as the amount of heat required to raise the temperature of 1 kg of the substance by 1°C.

The specific heat capacity is defined as the amount of heat required to raise the temperature of 1 kg of the substance by 1 degree Celsius.