623 is a root of f(x)=x2−11,532. Find the other roots of f(x).Write your answer as a list of simplified values separated by commas, if there is more than one value.
Q. 623 is a root of f(x)=x2−11,532. Find the other roots of f(x).Write your answer as a list of simplified values separated by commas, if there is more than one value.
Given root symmetry: Since 623 is a root, the other root will also be 623 because the roots of a quadratic equation are symmetric with respect to the y-axis when the coefficient of x is 0.
Product of roots: To find the other root, we use the fact that the product of the roots of a quadratic equation ax2+bx+c=0 is ac. Here, a=1 and c=−11,532.
Calculate product: The product of the roots is (623)×other_root=−11,532.
Solve for other root: Solve for the other root: other_root=623−11,532.
Simplify other root: Simplify the other root: other_root=623−11,532×(33)=62×3−11,5323.
Further simplify: Further simplify: other_root=186−11,5323.
Final other root: Divide to get the other root: other_root=−623.