Question

10x² + 19x - 1

Explanation:

Step1: Identify quadratic coefficients

For $ax^2+bx+c$, here $a=10$, $b=19$, $c=-1$

Step2: Apply quadratic formula

Quadratic formula: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
Substitute values:

$$ x=\frac{-19\pm\sqrt{19^2-4(10)(-1)}}{2(10)} $$

Step3: Calculate discriminant

Compute $b^2-4ac$:

$$ 19^2-4(10)(-1)=361+40=401 $$

Step4: Simplify final expression

Substitute discriminant back:

$$ x=\frac{-19\pm\sqrt{401}}{20} $$

Answer:

$x=\frac{-19+\sqrt{401}}{20}$ and $x=\frac{-19-\sqrt{401}}{20}$