Maths-
General
Easy

Question

Find the solution of the system of equations.
y equals negative x squared minus 2 x plus 9
Y = 3x+20

hintHint:

The quadratic formula corresponding to the equation a x squared plus b x plus c equals 0 text  is  end text fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction
We are asked to solve the given set of equation.

The correct answer is: We are asked to solve the given set of equation.


    Step 1 of 2:
    The LHS of the given set is equal. Hence, we can equate them. Thus, we get:
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 3 x plus 20 equals negative x squared minus 2 x plus 9 space space end cell row cell x squared plus 2 x plus 3 x plus 20 minus 9 equals 0 end cell row cell x squared plus 5 x plus 11 equals 0 space space space space space space space space space space space space space space end cell end table
    Step 2 of
    Solve the equation using the quadratic formula. Here, a equals 1 comma b equals 5 straight & c equals 11 text . That is,  end text
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction equals fraction numerator negative 5 plus-or-minus square root of 5 squared minus 4 left parenthesis 1 right parenthesis left parenthesis 11 right parenthesis end root over denominator 2 left parenthesis 1 right parenthesis end fraction end cell row cell equals fraction numerator negative 5 plus-or-minus square root of 25 minus 44 end root over denominator 2 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space end cell row cell equals fraction numerator negative 5 plus-or-minus square root of negative 19 end root over denominator 2 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space end cell end table
    Here, we get negative values in the root.
    So, we can conclude that the set has no real solutions.

    It is not necessary that every single quadratic equation would have two sets of real solution.

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