Chapter 6.7, Problem 1CYU

To determine

Solve the given equation. State the number and type of roots.

Answer to Problem 1CYU

The equation $x^2-3x-10=0$ has two roots, both are real 5,-2.

Explanation of Solution

Given information:

The equation $x^2-3x-10=0$ .

Formula used:

Splitting the middle term: To solve a quadratic equation $a{x}^2+bx+c=0$ , the middle term of equation is splitted in such a way that the product of coefficient of its parts is equal to product of coefficient of first and third term.

  $x^2-3x-10=0$

Recall that in splitting the middle term, the middle term of equation is splitted in such a way that the product of coefficient of its parts is equal to product of coefficient of first and third term.

  $\begin{array}{l}{x}^2-3x-10=0\\ \\ x^2-5x+2x-10=0\\ \\ x\left(x-5\right)+2\left(x-5\right)=0\\ \\ \left(x+2\right)\left(x-5\right)=0\end{array}$

By the above equation, we get that one or both terms $\left(x+2\right)$ and $\left(x-5\right)$ are zero,

Putting $\left(x+2\right)$ as zero,

  $\begin{array}{l}x+2=0\\ \\ x=-2\end{array}$

Putting $\left(x-5\right)$ as zero,

  $\begin{array}{l}x-5=0\\ \\ x=5\end{array}$

The equation $x^2-3x-10=0$ has two roots, both are real 5,-2.