Question

Mattie uses the discriminant to determine the number of zeros the quadratic equation 0 = 3x2 – 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 two zeros because the discriminant is greater than 0. The equation has no zeros because the discriminant is not a perfect square.

Answer 1

For $ax^2+bx+c=0$ the discriminant is $b^2-4ac$

there are 3 basic cases of what happens for different discriminants
1. if the discriminant is less than 0, then there are no real zeroes
2. if the discriminant is 0, then it has 1 zero
3. if the discriminant is greater than 0, it has 2 zeroes


so given
$0=3x^2-7x+4$
a=3,b=-7,c=4
thus the discriminant is $(-7)^2-4(3)(4)=49-48=1$
the discriminant is 1. 1 is positive, thus the equation has 2 zeroes because the discriminant is greater than 0

the answer is the equation has two zeroes because the discriminant is greater than 0

Answer 2

The equation has two zeros because the discriminant is greater than 0

An equation always has two zeroes unless the discriminant is 0 or negative.