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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)

23x2−12x−34=0 \frac{2}{3} x^{2}-\frac{1}{2} x-\frac{3}{4}=0 \newlineWhat is the sum of the solutions to the given equation?\newlineChoose 11 answer:\newline(A) −32 -\frac{3}{2} \newline(B) −34 -\frac{3}{4} \newline(C) 00\newline(D) 34 \frac{3}{4}

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Q. 23x2−12x−34=0 \frac{2}{3} x^{2}-\frac{1}{2} x-\frac{3}{4}=0 \newlineWhat is the sum of the solutions to the given equation?\newlineChoose 11 answer:\newline(A) −32 -\frac{3}{2} \newline(B) −34 -\frac{3}{4} \newline(C) 00\newline(D) 34 \frac{3}{4}
  1. Identify quadratic equation: Identify the quadratic equation and its standard form.\newlineThe given quadratic equation is (23)x2−(12)x−(34)=0(\frac{2}{3})x^2 - (\frac{1}{2})x - (\frac{3}{4}) = 0.\newlineA quadratic equation is generally given in the standard form ax2+bx+c=0ax^2 + bx + c = 0.
  2. Apply sum of roots formula: Apply the formula for the sum of the roots of a quadratic equation.\newlineThe sum of the roots of a quadratic equation ax2+bx+c=0ax^2 + bx + c = 0 is given by −ba-\frac{b}{a}.
  3. Calculate sum of roots: Calculate the sum of the roots using the coefficients from the given equation.\newlineFor the given equation (23)x2−(12)x−(34)=0(\frac{2}{3})x^2 - (\frac{1}{2})x - (\frac{3}{4}) = 0, a=23a = \frac{2}{3} and b=−12b = -\frac{1}{2}.\newlineThe sum of the roots is −(−12)/(23)-(-\frac{1}{2}) / (\frac{2}{3}).
  4. Simplify expression for sum of roots: Simplify the expression to find the sum of the roots.\newlineThe sum of the roots is (12)/(23)=(12)⋅(32)=34(\frac{1}{2}) / (\frac{2}{3}) = (\frac{1}{2}) \cdot (\frac{3}{2}) = \frac{3}{4}.

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