Write a quadratic equation having the given solutions.
-$7 \mathbf { i } , - 7 \mathbf { i }$
A) $x ^ { 2 } + 49 = 0$
B) $x ^ { 2 } - 14 i x + 49 = 0$
C) $x ^ { 2 } - 49 = 0$
D) $( x - 7 ) ^ { 2 } = 0$

Question

Quizplus · Accepted Answer

The correct quadratic equation is formed by using the sum and product of the roots. For roots $7i$ and $-7i$, the sum is $0$ and the product is $(-7i)(7i) = -49i^2 = 49$. Thus, the equation is $x^2 - (sum\ of\ roots)x + (product\ of\ roots) = 0$, which simplifies to $x^2 + 49 = 0$.

Write a Quadratic Equation Having the Given Solutions 7i,−7i7 \mathbf { i } , - 7 \mathbf { i }7i,−7i

Write a Quadratic Equation Having the Given Solutions $7 \mathbf { i } , - 7 \mathbf { i }$