The solution set for 2x^(2)-7x-4=0 is: (1) {2,-1} (3) {-2,1} (2) {-(1)/(2),4} (4) {(1)/(2),-4}

Identify Equation Type: Step 1: Identify the type of equation and its standard form. The equation 2x^2 - 7x - 4 = 0 is a quadratic equation in the standard form ax^2 + bx + c = 0, where a = 2, b = -7, and c = -4. Use Quadratic Formula: Step 2: Use the quadratic formula to find the roots. The quadratic formula is x = (-b ± sqrt(b^2 - 4ac)) / (2a). Plugging in the values: x = (-(-7) ± sqrt((-7)^2 - 4*2*(-4))) / (2*2) x = (7 ± sqrt(49 + 32)) / 4 x = (7 ± sqrt(81)) / 4 Simplify Square Root: Step 3: Simplify the square root and solve for x. x = (7 ± 9) / 4 x = (7 + 9) / 4 or (7 - 9) / 4 x = 16 / 4 or -2 / 4 x = 4 or -0.5

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Q. The solution set for

2 x^{2}-7 x-4=0

is:

\newline

(

1

)

\{2,-1\}

\newline

(

3

)

\{-2,1\}

\newline

(

2

)

\left\{-\frac{1}{2}, 4\right\}

\newline

(

4

)

\left\{\frac{1}{2},-4\right\}

Identify Equation Type: Step $1$ : Identify the type of equation and its standard form. $\newline$ The equation $2x^2 - 7x - 4 = 0$ is a quadratic equation in the standard form $ax^2 + bx + c = 0$ , where $a = 2$ , $b = -7$ , and $c = -4$ .
Use Quadratic Formula: Step $2$ : Use the quadratic formula to find the roots. $\newline$ The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ . Plugging in the values: $\newline$ $x = \frac{-(-7) \pm \sqrt{(-7)^2 - 4\cdot2\cdot(-4)}}{2\cdot2}$ $\newline$ $x = \frac{7 \pm \sqrt{49 + 32}}{4}$ $\newline$ $x = \frac{7 \pm \sqrt{81}}{4}$
Simplify Square Root: Step $3$ : Simplify the square root and solve for $x$ . $x = \frac{{7 \pm 9}}{{4}}$ $x = \frac{{7 + 9}}{{4}}$ or $\frac{{7 - 9}}{{4}}$ $x = \frac{{16}}{{4}}$ or $\frac{{-2}}{{4}}$ $x = 4$ or $-0.5$