which statement about the following equation is true? 3x² - 8x + 5 = 5x². the discriminant is less than 0…

which statement about the following equation is true? 3x² - 8x + 5 = 5x². the discriminant is less than 0, so there are two real roots. the discriminant is greater than 0, so there are two real roots. the discriminant is less than 0, so there are two complex roots. the discriminant is greater than 0, so there are two complex roots.

which statement about the following equation is true? 3x² - 8x + 5 = 5x². the discriminant is less than 0, so there are two real roots. the discriminant is greater than 0, so there are two real roots. the discriminant is less than 0, so there are two complex roots. the discriminant is greater than 0, so there are two complex roots.

Answer

Explanation:

Step1: Rearrange the equation

First, rewrite $3x^{2}-8x + 5=5x^{2}$ in standard - form $ax^{2}+bx + c = 0$. $3x^{2}-5x^{2}-8x + 5=0$, which simplifies to $-2x^{2}-8x + 5=0$. Here, $a=-2$, $b=-8$, and $c = 5$.

Step2: Calculate the discriminant

The discriminant formula is $\Delta=b^{2}-4ac$. Substitute $a=-2$, $b=-8$, and $c = 5$ into the formula: $\Delta=(-8)^{2}-4\times(-2)\times5$. $\Delta = 64+40$. $\Delta=104$.

Step3: Analyze the nature of the roots

Since $\Delta>0$, the quadratic equation has two real roots.

Answer:

The discriminant is greater than 0, so there are two real roots.