Exploring the Relationship between Roots and Coefficients of Quadratic Equations

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Questions and Answers

Which of the following statements correctly describes the relationship between the roots and coefficients of a quadratic equation?

  • The product of the roots is equal to the product of the coefficients.
  • The product of the roots is equal to the sum of the coefficients. (correct)
  • The sum of the roots is equal to the sum of the coefficients.
  • The sum of the roots is equal to the product of the coefficients.

What is the relationship between the roots and coefficients of a quadratic equation if the equation has only one real root?

  • The product of the roots is equal to the product of the coefficients.
  • The sum of the roots is equal to the product of the coefficients.
  • The sum of the roots is equal to the sum of the coefficients. (correct)
  • The product of the roots is equal to the sum of the coefficients.

What is the relationship between the roots and coefficients of a quadratic equation if the equation has no real roots?

  • The sum of the roots is equal to the product of the coefficients.
  • The sum of the roots is equal to the sum of the coefficients.
  • The product of the roots is equal to the product of the coefficients. (correct)
  • The product of the roots is equal to the sum of the coefficients.

Which of the following statements correctly describes the sum and product of the roots of a quadratic equation?

<p>The sum of the roots is equal to the coefficient of the linear term, and the product of the roots is equal to the constant term. (A)</p> Signup and view all the answers

What is the sum of the roots of the quadratic equation $2x^2+5x+3=0$?

<p>$-3$ (B)</p> Signup and view all the answers

What is the product of the roots of the quadratic equation $3x^2-7x+2=0$?

<p>$ rac{2}{3}$ (B)</p> Signup and view all the answers

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