Gr12 Mathematics: Ch 5.11 Solving Cubic Equations

What is the formula to find the roots of a quadratic equation?

x = -b ± √(b^2 + 4ac)/2a

x = -b ± √(b^2 - 4ac)/2a (correct)

x = ±√(b^2 - 4ac)/2a

x = b ± √(b^2 - 4ac)/2a

What is the purpose of the Factor Theorem in solving cubic equations?

To find the roots of the cubic equation directly

To solve the quadratic polynomial obtained after factorization

To find a potential root of the cubic equation by trial and error (correct)

To factorize the cubic polynomial into linear and quadratic factors

What is the expression for the cubic polynomial f(x) after finding a factor?

f(x) = (cx - d) · Q(x) (correct)

f(x) = (cx + d) + Q(x)

f(x) = (cx + d) / Q(x)

f(x) = (cx - d) × Q(x)

What is the last step in solving a cubic equation?

Combining the roots obtained from the factorization and quadratic polynomial Signup and view all the answers

How do you find the quadratic polynomial Q(x) in solving a cubic equation?

By dividing the cubic polynomial by the linear factor Signup and view all the answers

What is the purpose of solving the quadratic polynomial Q(x) in solving a cubic equation?

To find the final roots of the cubic equation Signup and view all the answers

What is the condition for the Factor Theorem to be applicable in solving cubic equations?

If f(d/c) = 0 Signup and view all the answers

What is the main purpose of dividing the cubic polynomial by a factor in solving cubic equations?

To get a quadratic polynomial Signup and view all the answers

What is the first step in solving a cubic equation using the factorization method?

Identify a factor of the polynomial by trial and error Signup and view all the answers

What is the relationship between the roots of the factor and the roots of the quadratic polynomial in solving a cubic equation?

They are the same roots Signup and view all the answers

What is the advantage of using the factorization method in solving cubic equations?

It is an algebraic method that can be used to find exact roots Signup and view all the answers

What is the role of the quadratic formula in solving cubic equations using the factorization method?

To find the roots of the quadratic polynomial Signup and view all the answers

Which of the following statements is true about the factorization method for solving cubic equations?

It involves finding a factor of the cubic polynomial using trial and error. Signup and view all the answers

What is the purpose of substituting potential roots into the polynomial when using the Factor Theorem?

To check if the polynomial can be expressed as a product of linear factors. Signup and view all the answers

Suppose we have a cubic polynomial (f(x) = ax^3 + bx^2 + cx + d), and we find a factor (cx - d). What can be concluded about the roots of the polynomial?

One root of the polynomial is (x = d/c). Signup and view all the answers

What is the relationship between the roots of the factor and the roots of the quadratic polynomial obtained after factorization?

One root of the factor is also a root of the quadratic polynomial. Signup and view all the answers

When using the factorization method, what is the purpose of solving the quadratic polynomial obtained after factorization?

To find the final solutions of the cubic equation. Signup and view all the answers

What is the main advantage of using the factorization method to solve cubic equations?

It is a more efficient method than using numerical methods. Signup and view all the answers