If the constant term in a quadratic equation is zero, prove that one of its roots is zero.

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Solution

Let quadratic equation is:
$\begin{matrix} a x^{2} + b x = 0 \Rightarrow x (a x + b) = 0 \Rightarrow x = 0, a x + b = 0 \Rightarrow a x = - b \Rightarrow x = \frac{- b}{a} \end{matrix}$
Here, Roots are 0 and $\frac{- b}{a} \Rightarrow$
One root is zero.
Hence proved.

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If the constant term in a quadratic equation is zero, prove that one of its roots is zero.

Let quadratic equation is: ax2+bx=0⇒x(ax+b)=0⇒x=0,ax+b=0⇒ax=−b⇒x=−baHere, Roots are 0 and −ba⇒One root is zero.Hence proved.

Let quadratic equation is:
$\begin{matrix} a x^{2} + b x = 0 \Rightarrow x (a x + b) = 0 \Rightarrow x = 0, a x + b = 0 \Rightarrow a x = - b \Rightarrow x = \frac{- b}{a} \end{matrix}$
Here, Roots are 0 and $\frac{- b}{a} \Rightarrow$
One root is zero.
Hence proved.