(2)/(3)x^(2)-(1)/(2)x-(3)/(4)=0 What is the sum of the solutions to the given equation? Choose 1 answer: (A) -(3)/(2) (B) -(3)/(4) (c) 0 (D) (3)/(4)

Identify quadratic equation: Identify the quadratic equation and its standard form. The given quadratic equation is (2/3)x^2 - (1/2)x - (3/4) = 0. A quadratic equation is generally given in the standard form ax^2 + bx + c = 0.Apply sum of roots formula: Apply the formula for the sum of the roots of a quadratic equation. The sum of the roots of a quadratic equation ax^2 + bx + c = 0 is given by -b/a.Calculate sum of roots: Calculate the sum of the roots using the coefficients from the given equation. For the given equation (2/3)x^2 - (1/2)x - (3/4) = 0, a = 2/3 and b = -1/2. The sum of the roots is -(-1/2) / (2/3).Simplify expression for sum of roots: Simplify the expression to find the sum of the roots. The sum of the roots is (1/2) / (2/3) = (1/2) * (3/2) = 3/4.

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(2)/(3)x^(2)-(1)/(2)x-(3)/(4)=0
What is the sum of the solutions to the given equation?
Choose 1 answer:
(A)
-(3)/(2)
(B)
-(3)/(4)
(c) 0
(D)
(3)/(4)

$\frac{2}{3} x^{2}-\frac{1}{2} x-\frac{3}{4}=0$ $\newline$ What is the sum of the solutions to the given equation? $\newline$ Choose $1$ answer: $\newline$ (A) $-\frac{3}{2}$ $\newline$ (B) $-\frac{3}{4}$ $\newline$ (C) $0$ $\newline$ (D) $\frac{3}{4}$

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Algebra 1

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Full solution

\frac{2}{3} x^{2}-\frac{1}{2} x-\frac{3}{4}=0

\newline

What is the sum of the solutions to the given equation?

\newline

Choose

1

answer:

\newline

(A)

-\frac{3}{2}

\newline

(B)

-\frac{3}{4}

\newline

(C)

0

\newline

(D)

\frac{3}{4}

Identify quadratic equation: Identify the quadratic equation and its standard form. $\newline$ The given quadratic equation is $(\frac{2}{3})x^2 - (\frac{1}{2})x - (\frac{3}{4}) = 0$ . $\newline$ A quadratic equation is generally given in the standard form $ax^2 + bx + c = 0$ .
Apply sum of roots formula: Apply the formula for the sum of the roots of a quadratic equation. $\newline$ The sum of the roots of a quadratic equation $ax^2 + bx + c = 0$ is given by $-\frac{b}{a}$ .
Calculate sum of roots: Calculate the sum of the roots using the coefficients from the given equation. $\newline$ For the given equation $(\frac{2}{3})x^2 - (\frac{1}{2})x - (\frac{3}{4}) = 0$ , $a = \frac{2}{3}$ and $b = -\frac{1}{2}$ . $\newline$ The sum of the roots is $-(-\frac{1}{2}) / (\frac{2}{3})$ .
Simplify expression for sum of roots: Simplify the expression to find the sum of the roots. $\newline$ The sum of the roots is $(\frac{1}{2}) / (\frac{2}{3}) = (\frac{1}{2}) \cdot (\frac{3}{2}) = \frac{3}{4}$ .