FINDING THE EQUATION Determine an equation which has roots at \( x=0 \) \( x=10 \). INSTRUCTION: Write the equation in standard form: \( x^{2}+b x+c=0 \). (The quadratic coefficient should be 1 .)

To find the equation with roots at \( x = 0 \) and \( x = 10 \), we start by using the fact that if \( r_1 \) and \( r_2 \) are the roots, then the equation can be represented as \( (x - r_1)(x - r_2) = 0 \). Substituting the roots gives us: \[ (x - 0)(x - 10) = 0 \implies x(x - 10) = 0. \] Expanding this results in: \[ x^2 - 10x = 0. \] However, to express it in standard form, we rewrite it as follows: \[ x^2 - 10x + 0 = 0. \] So, the final equation in standard form is: \[ x^2 - 10x + 0 = 0. \]