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Solve the quadratic equation below. If the solutions are not real, enter NA.

15x^(2)-x-2=0
The field below accepts a list of numbers or formulas separated by semicolons (e.g.
2;4;6
x+1;x-1). The order of the list does not matter.
To enter
sqrta, type
sqrt(a).

x=

$\newline$ Solve the quadratic equation below. If the solutions are not real, enter NA. $\newline$ $15 x^{2}-x-2=0$ $\newline$ The field below accepts a list of numbers or formulas separated by semicolons (e.g. $2 ; 4 ; 6$ $x+1 ; x-1)$ . The order of the list does not matter. $\newline$ To enter $\sqrt{a}$ , type $\operatorname{sqrt}(\mathrm{a})$ . $\newline$ $x=$

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Find the roots of factored polynomials

Full solution

Q.

\newline

Solve the quadratic equation below. If the solutions are not real, enter NA.

\newline

15 x^{2}-x-2=0

\newline

The field below accepts a list of numbers or formulas separated by semicolons (e.g.

2 ; 4 ; 6

x+1 ; x-1)

. The order of the list does not matter.

\newline

To enter

\sqrt{a}

, type

\operatorname{sqrt}(\mathrm{a})

.

\newline

x=

Identify coefficients: Identify the coefficients of the quadratic equation $15x^2 - x - 2 = 0$ . Here, $a = 15$ , $b = -1$ , and $c = -2$ .
Calculate discriminant: Calculate the discriminant using the formula $\Delta = b^2 - 4ac$ . For this equation, $\Delta = (-1)^2 - 4\cdot 15 \cdot (-2) = 1 + 120 = 121$ .
Determine roots: Since the discriminant $\Delta = 121$ is positive, there are two real and distinct roots.
Use quadratic formula: Calculate the roots using the quadratic formula, $x = \frac{-b \pm \sqrt{\Delta}}{2a}$ . Substituting the values, $x = \frac{-(-1) \pm \sqrt{121}}{2 \times 15}$ .
Simplify calculations: Simplify the calculations: $x = \frac{1 \pm 11}{30}$ . So, $x = \frac{1 + 11}{30} = \frac{12}{30} = 0.4$ and $x = \frac{1 - 11}{30} = \frac{-10}{30} = -\frac{1}{3}$ .

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