Question

9
TUI
If (x - 7)(x - p) = x2 - 12x + 35, then the value of p
is equal to
(2) 7
(1)
2​

Answer 1

Answer:

5.

Step-by-step explanation:

= > ( x - 7 )( x - p ) = x^2 - 12x + 35

= > ( x - 7 )( x - p ) = x^2 - ( 7 + 5 )x + 35

= > ( x - 7 )( x - p ) = x^2 - 7x - 5x + 35

= > ( x - 7 )( x - p ) = x( x - 7 ) - 5( x - 7 )

= > ( x - 7 )( x - p ) = ( x - 7 )( x - 5 )

= > ( x - p ) = x - 5

= > - p = - 5

= > p = 5

Hence the required value of p is 5.

Answer 2

♠♠Given, that♠♠:

(x–7)(x–p)=x²–12x+35

To Find:

Value of 'p'

♦♦Answer♦♦: (p)="5"

Solution:

On Factorising given RHS, we get:

i.e.,

RHS=x²–12x+35

Here, sum of zeroes=–12

product of zeroes=35

pair of such numbers=–7 and –5

So,

RHS=x²–7x–5x+35

or, =x(x–7)–5(x–7)

or, =(x–5)(x–7).[on taking out (x–7) as common]

Now, As,

(x–7)(x–p)=x²–12x+35

or(x–7)(x–p)=(x–7)(x–5)

• On comparing LHS with RHS, or on solving

x–p=x–5

–p=–5

p=5

Therefore, the value of 'p' is equal to '5'

Verification:

On solving LHS after substituting 5 for p, we get:

LHS=(x–7)(x–5)

or =(x)(x)–(5)(x)–(7)(x)–(7)(–5)

or =x²–5x–7x+35

» LHS=x²–12x+35=RHS

Hence, VERIFIED.