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if the equation 2ax*2-3bx+4c=0 and 3x*2-4x+5=0 have a common root, then a+b/b+c is equal to (a,b,c E R

if the equation 2ax*2-3bx+4c=0 and 3x*2-4x+5=0 have a common root, then a+b/b+c is equal to (a,b,c E R

Grade:12th pass

1 Answers

Harsh Tiwari
54 Points
2 months ago
Given that 2ax2 – 3bx + 4c = 0 and 3x2 – 4x + 5 = 0 have common roots.
 
3x2 – 4x + 5 = 0 has both roots imaginary.
 
2ax2 – 3bx + 4c = 0 also have same roots.
 
(2a / 3) = (- 3b / – 4) and (- 3b / – 4) = 4c / 5
 
(2a / 3) = (- 3b / – 4) and (- 3b / – 4) = 4c / 5
 
– 8a = – 9b and – 15b = – 16c
 
a = 9b / 8 and c = (15 / 16)b
 
[a + b] / [b + c] = [(9b / 8) + b] / [b + (15 / 16) b] = [(17 / 8) b / [31b / 16)] = 34 / 31

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