the quadratic equation x^2-6x+a=0 x^2-cx+6=0 have one root in common the other roots of the first and second equations are integers in the ratio 4:3 find the common root
Answer (1)
27th Dec, 2019
Hello Surjit,
Let α and β are roots of: x
2
- 6x + a = 0
Let α and γ are roots of: x
2
- cx + 6 = 0
So, α + β = 6 and α.β = a and α + γ = c and α.γ = 6 and β/γ = 4/3
α.β/α.γ = a/6
β/γ = a/6
a = 8
x
2
- 6x + a = 0
x
2
- 6x + 8 = 0
x = 2,6
But α.β = 8
hence α = 2
Answer is 2
Hope this Helps
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