Question

What are the solution(s) to the quadratic equation 40 − x2 = 0?

x = ±2Plus or minus 2 StartRoot 10 EndRoot
x = ±4Plus or minus 4 StartRoot 10 EndRoot
x = ±2Plus or minus 2 StartRoot 5 EndRoot
x = ±4Plus or minus 4 StartRoot 5 EndRoot

Answer 1

$\textbf{Given:}$

$40-x^2=0$

$\textbf{To find:}$

$\text{The roots of the given quadratic equation}$

$\textbf{Solution:}$

$\text{Consider,}$

$40-x^2=0$

$\implies\,x^2-40=0$

$\implies\,x^2-(\sqrt{40})^2=0$

$\text{Factorizing, using the identity}$

$\boxed{\bf\,a^2-b^2=(a-b)(a+b)}$

$(x-\sqrt{40})(x+\sqrt{40})=0$

$x=\pm\,\sqrt{40}$

$x=\pm\,\sqrt{4{\times}10}$

$\bf\,x=\pm\,2\sqrt{10}$

$\therefore\textbf{The roots of the given equation are \bf\,\pm\,2\sqrt{10} }$

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