Question

The roots of quadratic equation ax^2+bx=0 are

Answer 1

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Answer 2

The roots of the quadratic equation $ax^{2}+bx=0$ are $x=0,-\dfrac{b}{a}$.

Method 1.

Here, the given equation is

$ax^{2}+bx=0$

• We factorize the left hand side of the equation and then use the factors equalling to 0 to find the roots.

$\Rightarrow x(ax+b)=0$

Therefore either $x=0$ or $ax+b=0$

$\Rightarrow \Rightarrow x=0,-\dfrac{b}{a}$

Hence the roots of the given equation are

$x=0,-\dfrac{b}{a}$

Method 2.

Here, the given equation is

$ax^{2}+bx=0$

Using Sridhar Acharya's formula, we write

$x=\dfrac{-b\pm\sqrt{b^{2}-4\times a\times 0}}{2\times a}$

$=\dfrac{-b\pm\sqrt{b^{2}-0}}{2a}$

$=\dfrac{-b\pm b}{2a}$

$\Rightarrow x=0,-\dfrac{b}{a}$

Hence the roots of the given equation are

$x=0,-\dfrac{b}{a}$

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