Nature of the Roots

In a quadratic equation, what do you call the value b² −4ac?

• The Denominator

• The Diameter

• The discriminant

• The divisor

What is the nature of the roots of the quadratic equation if the value of its discriminant is zero?

• The roots are not real.

• The roots are real, rational and not equal.

• The roots are irrational and not equal

• The roots are real, rational and equal.

Which is true for the equation x²-5x+12=0?

• The roots are not real or imaginary.

• The roots are rational and not equal.

• he roots are irrational and not equal

• The roots are rational and equal.

Determine the nature of the roots of x²+7x+10=0?

• real, rational, and equal

• real, rational, and not equal

• real, irrational numbers and are not equal

• Imaginary

What are the nature of roots of the equation x² + 6x = -7?

• Real, rational and equal

• Real, irrational and unequal

• Real, rational and unequal

• Imaginary

Without solving the equation $3x^2$ − 4x + 2 = 0, what is the sum of the roots?

•  $\frac{-4}{\ \ \ \ 3}$  
  

•  $\frac{4}{3}$  

•  $\frac{-2}{\ \ 3}$  

•  $\frac{2}{3}$  

Without solving the equation 9x − 5 =  $3x^2$  
  give the sum and product of the roots.

•  $sum=3,\ product=\frac{5}{3}$  

  
  

• sum = -3 , product =  $\frac{-5}{3}$

• sum = -3, product =  $\frac{5}{3}$  

• sum = 3, product =  $\frac{-5}{3}$  

Write the quadratic equations whose roots have the given sum and product, sum = - 8, product = 5.

• x²+8x+5=0

• x²−8x+5=0

• x²−8x−5=0

• x²+5x−8=0

Write the quadratic equation whose roots are 2 and 3.

• x²+8x + 6 = 0

• x²− 5x + 6 = 0

• x² − 6x − 5 = 0

• x²+5x−8=0

 $Write\ the\ quadratic\ equation\ whose\ roots\ are\ 3\pm\sqrt{5}\$ .

•  $$x^2\ +5x\ +\ 3\ =\ 0 

•  

   $x^2\ -\ 9x\ +\ 5\ =\ 0$ 

•  $$x^2-4x-6=0$$ 

•  $$x^2-6x+4=0$$