If the equation x² + 4x + k has real and distinct roots, then

At present, Meenakshi's mother is twenty-five years older than her. Eight years ago, the product of their ages was 600. After how many years will Meenakshi's mother be 60 years old?

Find two consecutive positive integers, sum of whose squares is 365.

The discriminant of the quadratic equation x² - 4x + 4 = 0 is 

A lotus is 2 m above the water in a pond. Due to wind the lotus slides on the side and only the stem completely
submerges in the water at a distance of 10 m from the original position. Then the depth of water in the pond is

If the roots of the quadratic equation ax² + bx + c are sin α and cos α, then

If the sum of the squares of two consecutive positive even numbers is 340, then what is the sum of the two even numbers?

Two consecutive even integers are

Form a quadratic equation whose roots are 1 + √5 and 1 - √5.

The roots of the quadratic equation 6x² - x - 2 = 0 are