Question

What are the quadratic equations for x=-14​

Answer 1

Answer:

$x^{2} +14x=0$

Step-by-step explanation:

Given:

Given root is

$x=-14,\ 0$

Now we need to find the quadratic equation for given roots.

Solution:

The given roots are -14 and 0.

So, the sum of the roots.

$\alpha +\beta = -14 + 0$

$\alpha +\beta = -14$

Product of the given roots

$\alpha\times \beta = -14\times 0$

$\alpha\times \beta = 0$

Therefore, the required quadratic equation is.

$x^{2} -(\alpha +\beta )x+\alpha\times \beta=0$ -------------------(1)

Now we substitute $(\alpha +\beta )$ and $(\alpha\times \beta)$ in equation 1.

$x^{2} -(-14)x+0=0$

$x^{2} +14x=0$

Therefore, the quadratic equation for the given root is. $x^{2} +14x=0$