Maths-
General
Easy

Question

3 x to the power of 2 end exponent plus x minus 2 equals 0
The solutions to the quadratic equation above are a and b. What is the value of a + b ?

  1. negative fraction numerator 5 over denominator 3 end fraction  
  2. negative fraction numerator 1 over denominator 3 end fraction  
  3. fraction numerator 1 over denominator 3 end fraction  
  4. fraction numerator 5 over denominator 3 end fraction  

The correct answer is: negative fraction numerator 1 over denominator 3 end fraction


    HINT: Sum of solutions of any quadratic equation of the form a x to the power of 2 end exponent plus b x plus c equals 0 is fraction numerator negative b over denominator a end fraction.
    Complete step by step Solution
    Given quadratic equation is 3 x to the power of 2 end exponent plus x minus 2 equals 0.
    Given that solutions to the above quadratic equations are a and b.
    Here, a equals 3 comma b equals 1 and c equals negative 2.
    We know that sum of solutions of any quadratic equation of the form a x to the power of 2 end exponent plus b x plus c equals 0 is fraction numerator negative b over denominator a end fraction.
    On substituting the values in fraction numerator negative b over denominator a end fraction,
    we get fraction numerator negative b over denominator a end fraction equals fraction numerator negative 1 over denominator 3 end fraction.
    So, a plus b equals fraction numerator negative 1 over denominator 3 end fraction.
    Hence option B is the answer.
    Note: We can also solve this question using the quadratic formula fraction numerator negative b plus-or-minus square root of b to the power of 2 end exponent minus 4 a c end root over denominator 2 a end fraction.Here we get the solutions to be fraction numerator 2 over denominator 3 end fraction and negative 1. blankLet a equals fraction numerator 2 over denominator 3 end fraction and b equals negative 1.On adding a and b we get fraction numerator negative 1 over denominator 3 end fraction, which is the required solution.

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