Let $$f (x) = ax^2$$ and $$g(x) = bx^4$$ for any value of x. If $$a$$ and $$b$$ are positive constants, for how many values of $$x$$ is $$f (x) = g(x)$$ ?

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Uniteasy Admin · Accepted Answer

For a quartic equation,  it normally has four roots. But there're exceptions when it has duplicated root. In this case,
$$f (x) = g(x) \implies ax^2 = bx^4$$
Then
$$ax^2 - bx^4 = 0$$
$$x^2(a-bx^2) = 0$$
Then
$$x = 0$$, which represents two duplicate roots
or
$$x =\pm\sqrt{\dfrac{a}{b}  }  $$
There for there are three roots for the equation.
D is correct

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