Chapter 4.5, Problem 60HP

To determine

To explain: the quadratic equation cannot solve through factorization or factoring method.

Answer to Problem 60HP

The quadratic equation cannot be solved through factoring method since its product and sum cannot break middle term.

Explanation of Solution

Given: ${\text{x}}^{\text{2}}\text{+22x+121=246}$ .

Concept used:

The quadratic equation general formula is defined as:

  ${\text{x}}^{\text{2}}\text{+sx+p=0}$ .

Where s =sum of the two roots and p= product of two roots.

In factorization the midterm factorization can be done.

Calculation:

  ${\text{x}}^{\text{2}}\text{+22x+121=246}$ .

The equation can be written as:

  ${\text{x}}^{\text{2}}\text{+22x-125=0}$ .

By factorization:

Where the equation is defined by ${\text{x}}^{\text{2}}\text{+sx+p=0}$

Where s =sum of the two roots and p= product of two roots

If the two roots be $\text{a and b}$ then:

Sum of the roots = $\text{s=a+b}$ ; product of the roots= $\text{p=a×b}$

According to the given equation ${\text{x}}^{\text{2}}\text{+22x-125=0}$ and general equation ${\text{x}}^{\text{2}}\text{+sx+p=0}$ by comparing:

  $\text{s=22}$ , $\text{p=-125}$ .

here need to find 2 number whose sum is $\text{22}$ and product is $\text{-125}$

Which is not possible.

Hence, the quadratic equation cannot be solved through factoring method.