Question

Find the number of solutions of the equation 5x^2 + 3x - 7 = 0 by using the discriminant.

Answer 1

The discriminant is the part inside the root in the quadratic equation

`b^2-4ac`

if this expression gives a value equal to 0 then the equation has one real solution, if it gives a value greater than 0 then the equation has 2 real solutions and lastly if the values is less than 0 means that there are no real solutions.

a=5

b=3

c=-7

`\begin{gathered} b^2-4ac \\ (3)^2-4\cdot(5)\cdot(-7) \\ 9-(-140) \\ 9+140 \\ 149 \\ 149>0 \end{gathered}`

The equation has 2 real solutions.