Podcast
Questions and Answers
What is the nature of the roots of the quadratic equation x² + 4x + 0 = 0?
What is the nature of the roots of the quadratic equation x² + 4x + 0 = 0?
- Irrational
- Complex
- Rational and equal (correct)
- Rational and not equal
If one root of the equation x² + bx + c = 0 is equal to the square of the other root, then what is the value of b?
If one root of the equation x² + bx + c = 0 is equal to the square of the other root, then what is the value of b?
- 0 (correct)
- 1
- 2
- 10
What is the condition for the roots of the quadratic equation ax² + bx + c = 0 to be in the ratio m : n?
What is the condition for the roots of the quadratic equation ax² + bx + c = 0 to be in the ratio m : n?
- ma + bc(m + n)
- ma - bc(m + n)
- mb = ac(m + n) (correct)
- mb + ac(m - n)
If α and β are the roots of the equation x² + px + q = 0, then what is the value of α + β?
If α and β are the roots of the equation x² + px + q = 0, then what is the value of α + β?
If α and β are the roots of the equation x² - 7x + 10 = 0, then what is the value of αβ?
If α and β are the roots of the equation x² - 7x + 10 = 0, then what is the value of αβ?
What is the quadratic equation whose sum and product of the roots are -4 and 1, respectively?
What is the quadratic equation whose sum and product of the roots are -4 and 1, respectively?
Study Notes
Olympiad Math
- The roots of the quadratic equation x³ + 4x + 0 = 0 are 11 (rational and equal), 21 (rational and not equal), and 31 (irrational).
- For the equation 477+10+k+25 = 0, the value of k for which the roots are equal is 1, 18, or 21 ± √3.
- At 120°, the quadratic equation whose sum and product of the roots are -1 and f is x² - 4x + 1 = 0.
Quadratic Equations
- If a and b are the roots of the equation x² + 6 = 0, then (ab) is (4, 13), (-4, 13), or (4, -13).
- If a and b are the roots of the equation x² - 1 = 0, then a + b is 2, -2, or 4.
Roots of Equations
- The condition for the roots of the equation ax² + bx + c = 0 to be in the ratio m:n is bc = m(n+1).
- If one root is equal to the square of the other root of the equation x² + x - k = 0, then k = 1, 2, or -1.
- If a and b are the roots of the equation x² - x - b = 0, then 2 + l is 1, -1, or ±√2.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Solve quadratic equations and find the roots, sum, and product of roots. This quiz includes challenging questions from the Olympiad Tars book.
