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In simplest radical form, what are the solutions to the quadratic equation 0 = –3x2 – 4x + 5?

Quadratic formula: x = StartFraction negative b plus or minus StartRoot b squared minus 4 a c EndRoot Over 2 a EndFraction

x = negative StartFraction 2 plus or minus StartRoot 19 EndRoot Over 3 EndFraction
x = negative StartFraction 2 plus or minus 2 StartRoot 19 EndRoot Over 3 EndFraction
x = StartFraction 2 plus or minus StartRoot 19 EndRoot Over 3 EndFraction
x =


Sagot :

Answer:

Step-by-step explanation:

To find the solutions to the quadratic equation \( -3x^2 - 4x + 5 = 0 \) and express them in simplest radical form using the quadratic formula, we start by identifying the coefficients \( a = -3 \), \( b = -4 \), and \( c = 5 \).

The quadratic formula is:

\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

Substitute the values of \( a \), \( b \), and \( c \) into the formula:

\[ x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(-3)(5)}}{2(-3)} \]

Simplify the equation:

\[ x = \frac{4 \pm \sqrt{16 + 60}}{-6} \]

\[ x = \frac{4 \pm \sqrt{76}}{-6} \]

Now, simplify \( \sqrt{76} \):

\[ \sqrt{76} = \sqrt{4 \cdot 19} = 2\sqrt{19} \]

So the equation becomes:

\[ x = \frac{4 \pm 2\sqrt{19}}{-6} \]

Divide both terms in the numerator by -2:

\[ x = \frac{-2 \pm \sqrt{19}}{3} \]

Therefore, the solutions in simplest radical form are:

\[ x = \frac{-2 + \sqrt{19}}{3} \quad \text{and} \quad x = \frac{-2 - \sqrt{19}}{3} \]

Thus, the correct answer is:

\[ x = \frac{-2 \pm \sqrt{19}}{3} \]