Question

Which values of PPP and QQQ result in an equation with exactly one solution?

-5x+12=Px+Q−5x+12=Px+Q
Choose all answers that apply:

(Choice A)
A
P=5P=5P, equals, 5 and Q=12Q=12Q, equals, 12

(Choice B)
B
P=-5P=−5P, equals, minus, 5 and Q=-12Q=−12Q, equals, minus, 12

(Choice C)
C
P=5P=5P, equals, 5 and Q=-5Q=−5Q, equals, minus, 5

(Choice D)
D
P=-12P=−12P, equals, minus, 12 and Q=-12Q=−12

Answer 1

We are given equation : -5x+12=Px+Q.

Let us compare left and right sides of the equation.

On comparing Px = -5x.

Dividing both sides by x, we get

Px/x = -5x/x.

P = -5.

Let us compare other part of the given equation.

Q =12.

Therefore, we got P=-5 and Q =12.

Non of the given options seems correct.

Please check the option have P=-5 and Q =12.

Answer 2

Option A, C and D are correction Option.

Explanation:

Given Equation, -5x + 12 = Px + Q

We have to value of P and Q from given options such that equation has exactly one solution.

First simplify the equation,

-5x + 12 = Px + Q

-5x - Px = Q - 12

(-5 - P)x = Q - 12

from above P can not have value equal to -5 as if P = -5

we have (-5 - (-5))x = Q - 12

(-5 + 5)x = Q - 12

this equation has infinitely many solution as it removes x from the equation.

So, Option B is not our solution other than that All Options are our solution.

A).

P = 5 & Q = 12

⇒ (-5 - 5)x = 12 - 12

x = 0

C).

P = 5 & Q = -5

⇒ (-5 - 5)x = -5 - 12

-10x = -17

`x=(17)/(10)`

D).

P = -12 & Q = -12

⇒ (-5 - (-12))x = -12 - 12

7x = -24

`x=(-24)/(7)`

Therefore, Option A, C and D are correction Option.