Chapter 9.6, Problem 12CYU

To determine

Find the value of the discriminant and determine the number of real solution of the equation.

Answer to Problem 12CYU

The equation has two real solutions

Explanation of Solution

Given:

  $2x^2-11x+10=0$

Concept Used:

  $\text{The}\text{quadratic}\text{equation}:a{x}^2+bx+c=0,\text{then}\text{discriminant}:b^2-4ac$

Calculation:

  $\begin{array}{l}\text{The}\text{quadratic}\text{equation}:a{x}^2+bx+c=0,\text{then}\text{discriminant}:b^2-4ac\\ \text{Equation:}2x^2-11x+10=0\\ a=2;b=-11;c=10\\ $ \text{discriminant}:b^2-4ac={(-11)}^2-4·2·10=121-80=41$\end{array}$

Discriminant is 41 .

Since the discriminant is positive, the equation has two real solutions.

Thus, the equation has two real solutions