quadratic equation whose roots 6 and -5
You asked:
Construct a quadratic equation with roots \(6\) and \(-5\).
MathBot Answer:
\(x^{2} - x - 30 = 0\)
To find the quadratic equation from its roots, rewrite both of the given roots as factors.
$$\begin{aligned}x&=6\\x - 6&=0\end{aligned}$$ $$\begin{aligned}x&=-5\\ x + 5&=0\end{aligned}$$
Then construct the equation from these factors and expand.
$$\begin{aligned}(x - 6)(x + 5) &= 0\\ x^{2} - x - 30 &= 0\end{aligned}$$