Question

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.

Answer 1

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.