Question

Use the discriminant to find the nature of the solutions to the following quadratic equation3x^2 +x-3=0Two imaginary number solutionsone repeated rational solutionone repeated irrational number solution Two different irrational number solutionsTwo different rational number solutions.

Answer 1

Use the discriminant to find the nature of the solutions to the following quadratic equation

3x^2 +x-3=0



Two imaginary number solutions

one repeated rational solution

one repeated irrational number solution

Two different irrational number solutions

Two different rational number solutions.​

we know that

the discriminant of a quadratic equation is

`D=b^2-4ac`

we have

`3x^2+x-3=0`

so

a=3

b=1

c=-3

substitute in the equation Of discriminant

`\begin{gathered} D=(1^2)-4\cdot(3)\cdot(-3) \\ D=1+36 \\ D=37 \end{gathered}`

we have that

D >0

that means

Two different rational number solutions