Quadratic Equations Quiz

What is the nature of roots for the quadratic equation $9x^2 - 6x - 2 = 0$?

For the polynomial $p(x) = 6x^2 + 37x - (k - 2)$, if one zero is the reciprocal of the other, what is the value of $k$?

For the quadratic equation $5x^2 - 10x + k = 0$ to have real and equal roots, what should be the value of $k$?

If one root of the equation $3x^2 - 8x - (2k + 1) = 0$ is seven times the other, what is the value of $k$?

What is the quadratic equation whose roots are $(2 + oot{3})$ and $(2 - oot{3})$?

Quadratic Equations

Nature of roots: Determine if roots are real, equal, or complex for a quadratic equation (9x² - 6x - 2 = 0).
Reciprocal roots: If one root of a polynomial is the reciprocal of another, find the value of a constant (6x² + 37x - (k-2)).
Equal roots: Find the value of 'k' so that the quadratic equation has equal real roots (5x² - 10x + k = 0).
Roots in a proportion: If one root is a multiple of another, find the constant (3x² - 8x - (2k + 1)).
Quadratic equations from given roots: Construct a quadratic equation with given roots [(2+√3) and (2-√3)].
Roots of a quadratic equation: If 'a' and 'β' are roots of x² – 7x + 10 = 0, find the quadratic equation with roots a² and β²
Roots of a quadratic equation: Find the roots of x² +2√2x - 6 = 0
Sum of squares of the roots: Determine α² + β² for polynomial (5x² + 5x + 1)
Sum of reciprocals of the roots: Find α⁻¹ + β⁻¹ for polynomial (5x² + 5x + 1)

Water Tank Filling

Combined filling time: Two taps fill a tank in 9 3/8 hours; one tap takes 10 hours less than the other. Find the individual filling times.

Motorboat Speed

Upstream and downstream: A boat takes an hour longer to travel upstream vs downstream. Calculate the speed of the stream.

Test your knowledge on quadratic equations with various problems about nature of roots, equal roots, reciprocal roots, and constructing equations. This quiz will strengthen your understanding of quadratic functions and their properties.