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`        The quadratic equations x2 - 6x + a = 0 and x2 - cx + 6 = 0 have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then what is the common root?`
10 years ago

```							Let α and β are roots of:  x2 - 6x + a = 0
Let α and γ are roots of:  x2 - cx + 6 = 0
So, α + β = 6   ........ (i)
α.β = a    ........ (ii)
α + γ = c    ........ (iii)
α.γ = 6    ........ (iv)
β/γ = 4/3    ........ (v)
Now using (ii) and (iii)
α.β/α.γ = a/6
=> β/γ = a/6
=> using (v), 4/3 = a/6
=> So, a = 8
Now ,  x2 - 6x + a = 0
x2 - 6x + 8 = 0
x = 2 OR 6
As α.β = 8
So α = 2
```
10 years ago
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