quadratic equation whose roots 2 and -1/2
You asked:
Construct a quadratic equation with roots \(2\) and \(- \frac{1}{2}\).
MathBot Answer:
\(x^{2} - \frac{3 x}{2} - 1 = 0\)
To find the quadratic equation from its roots, rewrite both of the given roots as factors.
$$\begin{aligned}x&=2\\x - 2&=0\end{aligned}$$ $$\begin{aligned}x&=- \frac{1}{2}\\ x + \frac{1}{2}&=0\end{aligned}$$
Then construct the equation from these factors and expand.
$$\begin{aligned}(x - 2)(x + \frac{1}{2}) &= 0\\ x^{2} - \frac{3 x}{2} - 1 &= 0\end{aligned}$$