Podcast
Questions and Answers
What is the condition for a tangent to be parallel to the x-axis?
What is the condition for a tangent to be parallel to the x-axis?
- f'(x) = 0 (correct)
- f'(x) < 0
- f'(x) ≠ 0
- f'(x) > 0
If α is a root of the equation f(x) = 0, what can be said about the polynomial f(x)?
If α is a root of the equation f(x) = 0, what can be said about the polynomial f(x)?
- f(x) is exactly divisible by (x - α)²
- f(x) is exactly divisible by (x + α)
- f(x) is exactly divisible by (x - α) (correct)
- f(x) is exactly divisible by (x³ - α)
If the roots of the quadratic equations ax² + bx + c = 0 and a²x² + b²x + c² = 0 are the same, what can be said about b₁²/b₂²?
If the roots of the quadratic equations ax² + bx + c = 0 and a²x² + b²x + c² = 0 are the same, what can be said about b₁²/b₂²?
- b₁²/b₂² = a₂c₂/a₁c₁
- b₁²/b₂² = c₁/c₂
- b₁²/b₂² = a₁/a₂
- b₁²/b₂² = a₁c₁/a₂c₂ (correct)
If one root of the quadratic equation ax² + bx + c = 0 is k times the other root, what can be said about the equation?
If one root of the quadratic equation ax² + bx + c = 0 is k times the other root, what can be said about the equation?
What is the quadratic expression in x?
What is the quadratic expression in x?
If α and β are the roots of the quadratic equation ax² + bx + c = 0, then what is the sum of the roots?
If α and β are the roots of the quadratic equation ax² + bx + c = 0, then what is the sum of the roots?
If α and β are the roots of the quadratic equation ax² + bx + c = 0, then what is the product of the roots?
If α and β are the roots of the quadratic equation ax² + bx + c = 0, then what is the product of the roots?
What is the quadratic equation whose roots are α and β?
What is the quadratic equation whose roots are α and β?
What is the value of α² + β² in terms of the coefficients of the quadratic equation ax² + bx + c = 0?
What is the value of α² + β² in terms of the coefficients of the quadratic equation ax² + bx + c = 0?
What is the value of α³ + β³ in terms of the coefficients of the quadratic equation ax² + bx + c = 0?
What is the value of α³ + β³ in terms of the coefficients of the quadratic equation ax² + bx + c = 0?
If α and β are the roots of the equation x^2 - ax + b = 0, what is the value of α + β?
If α and β are the roots of the equation x^2 - ax + b = 0, what is the value of α + β?
If the roots of the equation x^2 - (α + β)x + αβ = 0 are a and b, what is the value of α and β?
If the roots of the equation x^2 - (α + β)x + αβ = 0 are a and b, what is the value of α and β?
If Vn = α^n + β^n, what is the value of Vn+1?
If Vn = α^n + β^n, what is the value of Vn+1?
If the roots of the equation (x - α)(x - β) + c = 0 are a and b, what is the relationship between α, β, a, and b?
If the roots of the equation (x - α)(x - β) + c = 0 are a and b, what is the relationship between α, β, a, and b?
If a and b are the roots of the quadratic equation x^2 + bx + c = 0, what is the value of a^2 + b^2 in terms of the coefficients?
If a and b are the roots of the quadratic equation x^2 + bx + c = 0, what is the value of a^2 + b^2 in terms of the coefficients?
If a quadratic equation has complex roots, what can be said about the discriminant?
If a quadratic equation has complex roots, what can be said about the discriminant?
What is the quadratic formula used to find?
What is the quadratic formula used to find?
If $α$ and $β$ are the roots of the equation $x^2 - ax + b = 0$, then what is the value of $α^2 + β^2$ in terms of $a$ and $b$?
If $α$ and $β$ are the roots of the equation $x^2 - ax + b = 0$, then what is the value of $α^2 + β^2$ in terms of $a$ and $b$?
If the roots of the equation $(x - α)(x - β) + c = 0$ are $a$ and $b$, then what is the value of $c$ in terms of $a$, $b$, $α$, and $β$?
If the roots of the equation $(x - α)(x - β) + c = 0$ are $a$ and $b$, then what is the value of $c$ in terms of $a$, $b$, $α$, and $β$?
If the roots of the equation $x^2 + ax + b = 0$ are $α$ and $β$, then what is the value of $αβ$ in terms of $a$ and $b$?
If the roots of the equation $x^2 + ax + b = 0$ are $α$ and $β$, then what is the value of $αβ$ in terms of $a$ and $b$?
If α and β are the roots of the quadratic equation x² - Sx + P = 0, which of the following is true?
If α and β are the roots of the quadratic equation x² - Sx + P = 0, which of the following is true?
If we replace x by 1/x in the quadratic equation ax² + bx + c = 0, what is the resulting equation?
If we replace x by 1/x in the quadratic equation ax² + bx + c = 0, what is the resulting equation?
If the quadratic equation x² - Sx + P = 0 has roots α and β, what is the equation whose roots are 1/α and 1/β?
If the quadratic equation x² - Sx + P = 0 has roots α and β, what is the equation whose roots are 1/α and 1/β?
If α and β are the roots of the quadratic equation x² - Sx + P = 0, what is the value of (α + β)²?
If α and β are the roots of the quadratic equation x² - Sx + P = 0, what is the value of (α + β)²?
If the quadratic equation ax² + bx + c = 0 has roots α and β, what is the equation whose roots are kα and kβ?
If the quadratic equation ax² + bx + c = 0 has roots α and β, what is the equation whose roots are kα and kβ?
If α and β are the roots of the equation x² - Sx + P = 0, then what is the equation whose roots are -α and -β?
If α and β are the roots of the equation x² - Sx + P = 0, then what is the equation whose roots are -α and -β?
If α and β are the roots of the equation ax² + bx + c = 0, then what is the equation whose roots are 1/α and 1/β?
If α and β are the roots of the equation ax² + bx + c = 0, then what is the equation whose roots are 1/α and 1/β?
If α and β are the roots of the equation x² - Sx + P = 0, then what is the value of (α - β)² in terms of S and P?
If α and β are the roots of the equation x² - Sx + P = 0, then what is the value of (α - β)² in terms of S and P?
If α and β are the roots of the equation ax² + bx + c = 0, then what is the equation whose roots are α² and β²?
If α and β are the roots of the equation ax² + bx + c = 0, then what is the equation whose roots are α² and β²?
If α and β are the roots of the equation x² - Sx + P = 0, then what is the value of α⁴ + β⁴ in terms of S and P?
If α and β are the roots of the equation x² - Sx + P = 0, then what is the value of α⁴ + β⁴ in terms of S and P?
