Identify the coefficients of the quadratic equation.

Question

Identify the coefficients of the quadratic equation.

Asked on March 28, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-03-28T21:51:06.860Z

Step 1: Identify the coefficients of the quadratic equation. The given equation is $3x^2 - 5x - 7 = 0$. Comparing this to the standard quadratic form $ax^2 + bx + c = 0$, we have: $a = 3$ $b = -5$ $c = -7$ Step 2: Write down the quadratic formula. The quadratic formula is: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ Step 3: Substitute the values of $a$, $b$, and $c$ into the formula. $$x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4(3)(-7)}}{2(3)}$$ Step 4: Simplify the expression. First, simplify the terms: $$x = \frac{5 \pm \sqrt{25 - (-84)}}{6}$$ $$x = \frac{5 \pm \sqrt{25 + 84}}{6}$$ $$x = \frac{5 \pm \sqrt{109}}{6}$$ Step 5: Write the two solutions for $x$. The two solutions are: $$x_1 = \frac{5 + \sqrt{109}}{6}$$ $$x_2 = \frac{5 - \sqrt{109}}{6}$$ The final answers are $\boxed{x = \frac{5 \pm \sqrt{109}}{6}}$.

Accepted Answer · 2026-03-28T21:51:06.860Z

Step 1: Identify the coefficients of the quadratic equation. The given equation is $3x^2 - 5x - 7 = 0$. Comparing this to the standard quadratic form $ax^2 + bx + c = 0$, we have: $a = 3$ $b = -5$ $c = -7$ Step 2: Write down the quadratic formula. The quadratic formula is: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ Step 3: Substitute the values of $a$, $b$, and $c$ into the formula. $$x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4(3)(-7)}}{2(3)}$$ Step 4: Simplify the expression. First, simplify the terms: $$x = \frac{5 \pm \sqrt{25 - (-84)}}{6}$$ $$x = \frac{5 \pm \sqrt{25 + 84}}{6}$$ $$x = \frac{5 \pm \sqrt{109}}{6}$$ Step 5: Write the two solutions for $x$. The two solutions are: $$x_1 = \frac{5 + \sqrt{109}}{6}$$ $$x_2 = \frac{5 - \sqrt{109}}{6}$$ The final answers are $\boxed{x = \frac{5 \pm \sqrt{109}}{6}}$.