AP EAMCET · Maths · Quadratic Equation
If the equations \(2 a x^2-3 b x+4 c=0\) and \(3 x^2-4 x+5=0\) have a common root, then \(\frac{a+b}{b+c}\) is equal to \((a, b, c \in \boldsymbol{R})\)
- A \(\frac{1}{2}\)
- B \(\frac{3}{35}\)
- C \(\frac{34}{31}\)
- D \(\frac{29}{23}\)
Answer & Solution
Correct Answer
(C) \(\frac{34}{31}\)
Step-by-step Solution
Detailed explanation
The discriminant of \(3 x^2-4 x+5=0\) is \(\Delta = (-4)^2 - 4(3)(5) = 16 - 60 = -44 Since the roots are complex and coefficients are real, and the equations have a common root, both equations must share the same roots. Thus, the equations are proportional:…
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