Question

Find the discriminant and determine the number of real solutions : 4x^2 + 7x - 15 = 0

Answer 1

The discriminant of a quadratic expression
`\displaystyle{ ax^2+bx+c` is

`\displaystyle{ D=b^2-4ac`.

In the quadratic
`4x^2+7x-15`, a=4, b=7, and c=-15.

Thus,
`\displaystyle{ D=b^2-4ac=7^2-4(4)(-15)=49+240=289>0`.


The discriminant is positive, this means that the equation has 2 real solutions.

Answer: 2