Podcast
Questions and Answers
What is the nature of roots for the quadratic equation $9x^2 - 6x - 2 = 0$?
What is the nature of roots for the quadratic equation $9x^2 - 6x - 2 = 0$?
- Two equal roots
- One real root
- Complex roots
- Two distinct real roots (correct)
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 polynomial $p(x) = 6x^2 + 37x - (k - 2)$, if one zero is the reciprocal of the other, what is the value of $k$?
- 8
- 15
- 12 (correct)
- 5
For the quadratic equation $5x^2 - 10x + k = 0$ to have real and equal roots, what should be 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 $k$?
- 0
- 20 (correct)
- 10
- 25
If one root of the equation $3x^2 - 8x - (2k + 1) = 0$ is seven times the other, what is 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 $(2 -
oot{3})$?
What is the quadratic equation whose roots are $(2 + oot{3})$ and $(2 - oot{3})$?
Flashcards
Nature of roots
Nature of roots
Describes the type of roots a quadratic equation has (real, equal, or imaginary)
Reciprocal roots
Reciprocal roots
If the roots of a quadratic equation are reciprocals of each other, the product of roots is 1. This relates to the constant term of the equation.
Real and equal roots
Real and equal roots
Roots of a quadratic equation that are identical real values.
Roots of quadratic equation
Roots of quadratic equation
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Quadratic equation with given roots
Quadratic equation with given roots
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Study Notes
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.
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