Question

If (x-2) is a common factor of expression x2+ax+b and x2+cx+d, then the value of b-d/c-a

Answer 1

Hey friend!

Here is your solution!
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x−2 is a common factorx−2=0

⇒x=2 is roots of both equation


x2 +ax+b=0
and
x2+cx+d=0
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Subtract two equations

x2+ax+b−x2−cx−d==0

⇒ax−cx+b−d=0

⇒b−d=cx−ax

⇒(b−d) = x(c−a)

⇒b−d / c−a=x
But x=2 is the common root

⇒b−d / c−a= 2

Hope it's helpful

Answer 2

Answer:

The value of $\frac{b-d}{c-a}$ is $2$.

Step-by-step explanation:

Given equations,

$x^{2} + ax + b$, be the equation $(1)$.

$x^{2} + cx + d$, be the equation $(2)$.

It is given that, $x - 2$ is the factor for both above equations.

• Thus, $x = 2$ is substituted in both the equations and then equated to zero.

Therefore,

• Equation $(1)$ implies, $(2^{2} ) + a(2) + b = 0$

                                                 $4 + 2a + b = 0$

• Equation $(2)$ implies, $(2^{2} ) + c(2) + d = 0$

                                                 $4 + 2c + d = 0$

On equating simplified equations of $(1)$ and $(2)$,

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

     $2a + b = 2c + d$

      $b - d = 2c -2a$

      $b - d = 2(c - a)$

         $\frac{b - d}{c - a } = 2$.

Thus, when $(x-2)$ is the common factor for $x^{2} + ax + b$ and $x^{2} + cx + d$, $\frac{b - d}{c - a }$ is equal to $2$.