Question

Maltie uses the discriminant to determine the number of zeros the quadratic equation 0 : 3x? - 7x + 4 has. Which best

describes the discriminant and the number of zeros?
The equation has one zero because the discriminant is 1.
The equation has one zero because the discriminant is a perfect square
The equation has iwo zeros because the discriminant is greater than 0.
The equation has no zeros because the discriminant is not a perfect square.

Answer 1

The equation has two zeros because the discriminant is greater than zero.

Explanation:

This is the equation to solve:

`0=3x^2-7x+4`

Recall that the discriminant is the formulation of the quantity that appears inside the square root in the quadratic formula that solves the above quadratic equation. In the quadratic formula, you have a rational number plus or minus the square root of the discriminant we are talking about, divided by a factor. Therefore, as long as the discriminant is not zero, you will have two possible solutions to the equation : one with the plus - when you add, and the other one when you subtract (use the minus option).

The discriminant in this case is given by:
`(-7)^2-4\,(3)\,(4)\,=\, 49-48=1`

Square root of 1 is 1 , so in one case you add , and the other one when you subtract this value. A total of two zeros for the equation.

Therefore, the most appropriate answer would be:

The equation has two zeros because the discriminant is greater than zero.