Chapter 9.3, Problem 47PFA

(a)

To determine

The solution that are related to the equation is c=-3 and y=0.

Answer to Problem 47PFA

It has two possible solutions.

Explanation of Solution

Given information:

The given function s is

  $y=x^2-2x+c$

Formula used:

  $b^2-4ac>0$

Calculation:

  $c=-3y=0$

Now to check the number of solution to check the discriminate,

i.e.

if $b^2-4ac>0\to \text{two solution}$

if $b^2-4ac=0\to \text{one solution}$

if $b^2-4ac<0\to \text{No solution}$

Put $c=-3\&y=0\text{in}\text{=n}\left(i\right)$

Hence,

  $\begin{array}{l}0=x^2-2x-3\\ x^2-2x-3=0\\ b^2-4ac={\left(-2\right)}^2\times 4\times 1\times \left(-3\right)\\ =4+12\\ =16\left(\text{Positive}\right)\end{array}$

Two solutions

Conclusion:

It has two possible solutions.

(b)

To determine

The solution that are related to the equation is c=-2 and y=-3.

Answer to Problem 47PFA

It contains one solution.

Explanation of Solution

Given information:

The given function s is

  $y=x^2-2x+c$

Formula used:

  $b^2-4ac$

Calculation:

Put c =-3 & y = -3 in = 4(i)

  $\begin{array}{l}-3=x-2x-2\\ or{x}^2-2x-2+3=0\\ or{x}^2-2x+1=0\end{array}$

  $\begin{array}{l}{b}^2-4ac={\left(-2\right)}^2-4\times 1\times 1\\ =0\end{array}$

One solution

Conclusion:

It contains one solution.

(c)

To determine

The value of c when y=0.

Answer to Problem 47PFA

The Option C and Option E is correct

Explanation of Solution

Given information:

The given function s is

  $y=x^2-2x+c$

Formula used:

  $b^2-4ac$ must be negative

Calculation:

  $\text{put}y=0in=n(i)$

  $\begin{array}{l}0=x^2-2x+c\\ or{x}^2-2x+c=0\\ b^2-4ac={\left(-2\right)}^2-4\times 1\times c\\ =4-4\times c\end{array}$

Now having n solution $b^2-4ac$ must be negative

Option C and Option E is correct

Conclusion:

The Option C and Option E is correct