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TS EAMCET · Maths · Quadratic Equation

If \((x-2)\) is a common factor of the expressions \(x^2+a x+b\) and \(x^2+c x+d\), then \(\frac{b-d}{c-a}\) is equal to

  1. A \(-2\)
  2. B \(-1\)
  3. C \(1\)
  4. D \(2\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(2\)

Step-by-step Solution

Detailed explanation

Since, \((x-2)\) is a common factor of the expressions \(x^2+a x+b\) and \(x^2+c x+d\) \(\Rightarrow \quad 4+2 a+b=0\) ...(i) and \(4+2 c+d=0\) ...(ii) \(\begin{array}{rlrl}\Rightarrow & 2 a+b =2 c+d \\ \Rightarrow & b-d =2(c-a) \\ \Rightarrow & \frac{b-d}{c-a} =2\end{array}\)