Question

which of the statements about the following quadratic equation is true? 6x² - 8 = 4x² + 7x the discriminant is greater than zero, so there are two real roots. the discriminant is greater than zero, so there are two complex roots the discriminant is less than zero, so there are two real roots the discriminant is less than zero, so there are two complex roots

Explanation:

Step1: Rearrange to standard form

$$6x^2 - 8 - 4x^2 - 7x = 0$$
$$2x^2 - 7x - 8 = 0$$

Step2: Identify coefficients

For $ax^2+bx+c=0$, $a=2$, $b=-7$, $c=-8$

Step3: Calculate discriminant

$$\Delta = b^2 - 4ac = (-7)^2 - 4(2)(-8)$$
$$= 49 + 64 = 113$$

Step4: Analyze discriminant

$\Delta=113>0$, so two real roots.

Answer:

A. The discriminant is greater than zero, so there are two real roots.