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Here, we are required to find out how many solutions to start out seeking while solving a quadratic equation and the condition for a quadratic graph not having zeros ( no x-intercepts).
Therefore, where X³ occurs in an equation, it is cubic and consequently has 3 solutions.
And, a quadratic equation can have no zeros ( no x intercepts) if the roots of the equation are complex numbers.
A quadratic equation is one which has the highest degree of its independent variable ( usually x) to be 2.
Consequently, when we solve a quadratic equation, one should start out seeking two (2) solutions.
This is so because, the number of solutions to start out seeking corresponds with the highest power of the independent variable, X.
Therefore, where X³ occurs in an equation, it is cubic and consequently has 3 solutions.
Therefore, where X¹ occurs in an equation, it is linear and consequently has 1 solution.
And, where X² occurs in an equation, it is quadratic and consequently has 2 solutions.
It is possible to have a quadratic equation with no zeros (i.e no x-intercepts)
The explanation for the situation above is caused by complex roots.
When the roots of a quadratic equation is in the form x = a ± √-b
Ultimately, the roots of the equation becomes
x = a ± i√b.
Where i = √-1.
Therefore, for a quadratic equation, we start out seeking 2 solutions.
And, a quadratic equation can have no zeros ( no x intercepts) if the roots of the equation are complex numbers.
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