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Question
Use the discriminant to determine the number and type of solutions of the following quadratic equation.
-7x²-5x+5=0
Select the correct answer below:
O There are two distinct rational solutions.
O There are two distinct irrational solutions.
O There are two complex solutions.
O There is a single rational solution.

Respuesta :

Hi

A standard quadric equation is :  ax² +bx +c = 0

discriminant  is :  b² -4*a*c  

3 cases can occur :  

Discriminant is strictly positive , then equation has two Real solutions.  

If discriminant is equal at 0 , there  is one solution ( to be honest, there is 2 identical solutions )

If discriminant is negative, so there is  2 imaginary / complex solutions.

So :

 -7x² -5x +5 = 0

here :  a = -7 ; b = -5 and c = 5

So discriminant :  dis =   (-5)²- 4 *(-7) * ( 5)

                                 =   25 - 4*-35

                                  =  25 + 140

                                  = 165

165 is strictly superior to 0, so the equation has two real solutions.

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