30 Questions
What is the condition for a tangent to be parallel to the x-axis?
f'(x) = 0
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)
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 = a₁c₁/a₂c₂
If one root of the quadratic equation ax² + bx + c = 0 is k times the other root, what can be said about the equation?
(k + 1)²b² = kac
What is the quadratic expression in x?
ax² + bx + c
If α and β are the roots of the quadratic equation ax² + bx + c = 0, then what is the sum of the roots?
-b/a
If α and β are the roots of the quadratic equation ax² + bx + c = 0, then what is the product of the roots?
c/a
What is the quadratic equation whose roots are α and β?
x² - (α + β)x + αβ = 0
What is the value of α² + β² in terms of the coefficients of the quadratic equation ax² + bx + c = 0?
b² - 4ac
What is the value of α³ + β³ in terms of the coefficients of the quadratic equation ax² + bx + c = 0?
b(b² - 3ac)
If α and β are the roots of the equation x^2 - ax + b = 0, what is the value of α + β?
a
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?
α and β
If Vn = α^n + β^n, what is the value of Vn+1?
aVn + bVn-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?
α + β = a + 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?
b^2 - 4c
If a quadratic equation has complex roots, what can be said about the discriminant?
It is a negative number.
What is the quadratic formula used to find?
The roots of a quadratic equation.
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 $b$?
$a^2 - 2b$
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 $β$?
$ab - αβ$
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 $b$?
$b/a$
If α and β are the roots of the quadratic equation x² - Sx + P = 0, which of the following is true?
α + β = S and αβ = P
If we replace x by 1/x in the quadratic equation ax² + bx + c = 0, what is the resulting equation?
cx² + bx + a = 0
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?
cx² + bx + a = 0
If α and β are the roots of the quadratic equation x² - Sx + P = 0, what is the value of (α + β)²?
S² - 2P
If the quadratic equation ax² + bx + c = 0 has roots α and β, what is the equation whose roots are kα and kβ?
ax² + kbx + k²c = 0
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?
ax² - Sx - P = 0
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?
cx² + bx + a = 0
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?
S² - 4P
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?
a(x² - bx + c) = 0
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?
(S² + P²)² - 2P(S³ + P)
Test your understanding of quadratic equations and inequations with this quiz. Learn about the graphical representation, roots, and properties of quadratic equations. Evaluate your knowledge of quadratic equations and inequations.
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