Chapter 5.3, Problem 57PPS

To determine

To calculate: The quadratic equation in standard form with given roots $3.4,0.6$ .

Answer to Problem 57PPS

The standard form of the quadratic equation is $25x^2-100x+51=0$ .

Explanation of Solution

Given information:

The roots $3.4,0.6$ .

Formula used:

If a and b are two roots of a quadratic equation then standard form of the equation is given by $x^2-\left(a+b\right)x+ab=0$ , where $a+b$ represents sum of roots and $ab$ is product of roots.

Calculation:

Consider the given roots $3.4,0.6$ .

Recall that if a and b are two roots of a quadratic equation then standard form of the equation is given by $x^2-\left(a+b\right)x+ab=0$ , where $a+b$ represents sum of roots and $ab$ is product of roots.

Apply it,

  $\begin{array}{c}{x}^2-\left(3.4+0.6\right)x+\left(3.4\times 0.6\right)=0\\ x^2-4x-\frac{51}{25}=0\\ 25x^2-100x+51=0\end{array}$ .

Thus, the standard form of the quadratic equation is $25x^2-100x+51=0$ .