which statement about the following equation is true? 2x² - 9x + 2 = -1 the discriminant is less than 0, so…

which statement about the following equation is true? 2x² - 9x + 2 = -1 the discriminant is less 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 real roots. the discriminant is greater than 0, so there are two complex roots.

which statement about the following equation is true? 2x² - 9x + 2 = -1 the discriminant is less 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 real roots. the discriminant is greater than 0, so there are two complex roots.

Answer

Explanation:

Step1: Rewrite the equation in standard form

First, rewrite $2x^{2}-9x + 2=-1$ as $2x^{2}-9x+3 = 0$. For a quadratic equation $ax^{2}+bx + c = 0$, here $a = 2$, $b=-9$, $c = 3$.

Step2: Calculate the discriminant

The discriminant formula is $\Delta=b^{2}-4ac$. Substitute $a = 2$, $b=-9$, $c = 3$ into it: $\Delta=(-9)^{2}-4\times2\times3=81 - 24=57$.

Step3: Analyze the nature of the roots

Since $\Delta = 57>0$, the quadratic - equation has two real roots.

Answer:

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