Gr12 Mathematics: Ch 5.11 Solving Cubic Equations

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Questions and Answers

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?

<p>Combining the roots obtained from the factorization and quadratic polynomial (C)</p> Signup and view all the answers

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

<p>By dividing the cubic polynomial by the linear factor (D)</p> Signup and view all the answers

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

<p>To find the final roots of the cubic equation (A)</p> Signup and view all the answers

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

<p>If f(d/c) = 0 (B)</p> Signup and view all the answers

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

<p>To get a quadratic polynomial (B)</p> Signup and view all the answers

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

<p>Identify a factor of the polynomial by trial and error (A)</p> 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?

<p>They are the same roots (C)</p> Signup and view all the answers

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

<p>It is an algebraic method that can be used to find exact roots (D)</p> Signup and view all the answers

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

<p>To find the roots of the quadratic polynomial (A)</p> Signup and view all the answers

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

<p>It involves finding a factor of the cubic polynomial using trial and error. (A)</p> Signup and view all the answers

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

<p>To check if the polynomial can be expressed as a product of linear factors. (D)</p> 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?

<p>One root of the polynomial is (x = d/c). (D)</p> 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?

<p>One root of the factor is also a root of the quadratic polynomial. (B)</p> Signup and view all the answers

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

<p>To find the final solutions of the cubic equation. (C)</p> Signup and view all the answers

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

<p>It is a more efficient method than using numerical methods. (B)</p> Signup and view all the answers

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