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?
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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.
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