Question

solve this......................................​

Answer 1

Answer:

correct answer is 2.

if you let in the first equation =(x-2) (x+3)

and second equation =(x-2) (x-4)

then we get

a=1, b=-6, c=-6 & d=8

then we calculate

-14/-7 = 2

and find the answer 2.

Answer 2

Step-by-step explanation:

Given : $(x-2)$ is a common factor of two expressions $x^{2} +ax+b$ and  $x^{2} +cx+d$.

To find : The value of  $\frac{b-d}{c-a}$.

• Calculation for value of $\frac{b-d}{c-a}$ :

We have two quadratic equations,

$x^{2} +ax+b=0$          ---(1)

$x^{2} +cx+d=0$          ---(2)

and $(x-2)$ is the common factor of both these given equations.

$x-2=0$

$x=2$

by putting the value of x in equations (1) and (2),

from equation (1),                              from equation (2),

$(2)^2+2*x+b=0$                               $(2)^2+2*c+d=0$  

$4+2a+b=0$                                          $4+2c+d=0$  

 $2a+b=-4$                 ---(3)                     $2c+d=-4$               --(4)

As the R.H.S of equations (3) and (4) are same so we can equate them.

by equating equations (3) and (4),

⇒  $2a+b=2c+d$

taking d to L.H.S and 2a to R.H.S,

⇒  $b-d=2c-2a$

⇒  $b-d=2(c-a)$

taking $(c-a)$ to denominator of L.H.S,

⇒  $\frac{b-d}{c-a}=2$

Hence we get the value of  $\frac{b-d}{c-a}$ is option (d) 2.