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  • Quadratic Equations, Inequalities, and Functions
  • Quadratic function and discriminant
  • Discriminant of a quadratic equation

Discriminant of a quadratic equation

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  • Question 1:
    1 pts
    		Discriminant of the quadratic polynomial $ax^2 + bx + c$ is $$D=b^2-4ac$$
  • Question 2:
    1 pts
    		The discriminant of quadratic equation $x^2-3x+2=0$ is:

    $1$

    $2$

    $3$

    $4$

  • Question 3:
    1 pts
    		The discriminant of quadratic equation $2x^2-3=0$ is:

    $24$

    $-24$

    $12$

    $-12$

  • Question 4:
    1 pts
    		The discriminant of quadratic equation $x^2=0$ is:

    $-1$

    $0$

    $1$

    $2$

  • Question 5:
    1 pts
    		If the discriminant of an equation is $> 0$, which of the following is true
    Equation has two complex solutions
    Equation has one real solution
    Equation has two real solutions
  • Question 6:
    2 pts
    		Let $D$ be a discriminant of the quadratic equation which graph is shown at the right. Which of the following statements is true?
    $D>0$
    $D<0$
    $D=0$
  • Question 7:
    2 pts
    		If the discriminant is a perfect square the roots are rational.
  • Question 8:
    2 pts
    		How many and what type of solutions would an equation have if the discriminant is 1234?
    two complex solutions
    one real solution
    two real solutions
  • Question 9:
    2 pts
    		State the nature of the roots of the following quadratic equations $2x^2-5x+4=0$
    two complex solutions
    one real solution
    two real solutions
  • Question 10:
    3 pts
    		Let $D$ be a discriminant of the quadratic function $f(x)=ax^2+bx+c$ , which graph is shown at the right. Which of the following statements is true?
    a>0 , D>0
    a<0 , D<0
    a>0 , D<0
    a<0 , D>0
  • Question 11:
    3 pts
    		Let $D$ be a discriminant of the quadratic function $f(x)=ax^2+bx+c$ , which graph is shown at the right. Which of the following statements is true?
    $a<0 , D>0 , c>0$
    $a>0 , D>0 , c<0$
    $a<0 , D<0 , c>0$
  • Question 12:
    3 pts
    		If the value of a discriminant is a perfect square, then the quadratic polynomial can be factored.
  • Question 13:
    3 pts
    		If the value of a discriminant is zero, then the quadratic polynomial is a perfect square.
  • Question 14:
    3 pts
    		Determine $k$ so that $x^2-10x+k=0$ has two equal real solutions.

    $10$

    $15$

    $20$

    $25$

  • Question 15:
    3 pts
    		Determine $k$ so that $kx^2-2kx+1=0$ has two equal real solutions.

    $k = 1 \, or\, k = 0$

    $k = 0$

    $k = 1$

    $k = 2 \,or \, k = 0$

Solving quadratic equations

Graphing function and discriminant