Question

are factors of
If both (x - 2) and (x - 1)
px2 + 5x + r, then​

Answer 1

Answer:

The given polynomial is Q(x)=px

2

+5x+r

It is also given that (x−2) and (x−

2

1

​

) are the factors of Q(x) which means that Q(2)=0 and Q(

2

1

​

)=0.

Let us first substitute Q(2)=0 in Q(x)=px

2

+5x+r as shown below:

Q(x)=px

2

+5x+r

⇒Q(2)=p(2)

2

+(5×2)+r

⇒0=(p×4)+10+r

⇒0=4p+10+r

⇒4p+r=−10.........(1)

Now, substitute Q(

2

1

​

)=0 in Q(x)=px

2

+5x+r as shown below:

Q(x)=px

2

+5x+r

⇒Q(

2

1

​

)=p(

2

1

​

)

2

+(5×

2

1

​

)+r

⇒0=

4

p

​

+

2

5

​

+r

⇒0=

4

p+(5×2)+(r×4)

​

⇒0=

4

p+10+4r

​

⇒0×4=p+10+4r

⇒0=p+10+4r

⇒p+4r=−10.........(2)

Now subtracting the equations (1) and (2), we get

(4p−p)+(r−4r)=−10−(−10)

⇒3p−3r=−10+10

⇒3p−3r=0

⇒3p=3r

⇒p=r

Hence, p=r is proved.

Step-by-step explanation:

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Answer 2

Answer:

Mark upper one as brainlist plz