# Problem 1087

Use the discriminant to find what type of solutions the equation has. Do not solve the equation.

3x2 + 7x + 4 =0

Solution:-

The dixcriminate is the radicand in the quadratic formula, b2 – 4ac. If the value of the discriminant is a positive number that is also a perfect square, then the equation has two different rational solutions.

If the value of the discriminant is positive number that is not a perfect square, then the equation has two different irrational solutions.

If the value of the discriminant is equal to zero, then the equation has one rational solution.

If the value of the discriminant is a negative number, then the equation has two nonreal complex solutions.

Now that the equation is in the standard form if ax2 + bx + c, find the values for a, b, and c.

The values are a = 3, b = 7, and c = 4.

Substitute a = 3 , b = 7, and c = 4.

b2-4ac = (7)2 – 4(3)(4)

Simplify the expression.

(7)2 – 4 (3)(4) = 1

The discriminant is 1. Based on the result, the equation has two different rational solutions because the discriminant is positive that is a perfect square.