Answer:
Since discriminant is positive, therefore, the given quadratic equation has two real solutions. Correct answer is the last option.
Step-by-step explanation:
We have been given a quadratic equation and we need to figure out the number of real solutions of the equation.
[tex]2x^{2}+7x-15=0[/tex]
We know that discriminant of a general quadratic equation [tex]ax^{2}+bx+c=0[/tex] is given by [tex]D=b^{2}-4ac[/tex]
For the given quadratic equation [tex]2x^{2}+7x-15=0[/tex], we have [tex]a=2,b=7,c=-15[/tex]. Upon substituting these values in the formula for discriminant, we get:
[tex]D=7^{2}-4(2)(-15)[/tex]
[tex]D=49+120[/tex]
[tex]D=169[/tex]
Since discriminant is a positive number, therefore, the given quadratic equation has two real solutions. Hence, the last option is the correct answer.
