Question

under what conditions will ax²+bx+c=0 not be a quadratic equations​

Answer 1

Answer:

When a ≠ 0 then the ax²+ bx + c = 0 not be a quadratic polynomial..

As if the a = 0 then the equation

ax²+ bx + c = 0 become linear equation..

Thank you

Answer 2

Answer:

If $x$ solves $ax^2+bx+c=0$, then it also solves $x^2+\frac{b}{a}x+\frac{c}{a} = 0$, which we obtain by just dividing through by $a$.

Let the roots of this polynomial be $x_1$ and $\frac{1}{x_1}$. Writing the polynomial in terms of factors, we get

$$(x-x_1)(x-\frac{1}{x_1}) = x^2+\frac{b}{a}x+\frac{c}{a}.$$

Expanding on the left hand side, this becomes

$$x^2-\left(x_1+\frac{1}{x_1}\right)x+1 - x^2+\frac{b}{a}+\frac{c}{a}.$$

Therefore, we must have $\frac{c}{a} = 1$, implying $c = a$. We do not need to care about $b$.