Question

The quadratic equation x^2-6x+a=0 and x^2-cx+6=0 have one root in common. the other roots of first and second equations are in the ratio 4:3 .then the common root is?

Answer 1

Let the common root of the given quadratic equation be α the other of equation x2 –6x + a = 0 be β and for x2– cx + 6 = 0 be γ.

For x2 –6x + a = 0


For x2 – cx + 6 = 0


On dividing (2) by (3), we get


So, from (2), αβ = 8

and from (1) α + β = 6

⇒ β = 6 – α

⇒ α (6 – α) = 8

⇒ 6α – α2 = 8

⇒ α2 – 6α + 8 = 0

⇒ α2 – 4α – 2α + 8 = 0

⇒ (α – 4) (α – 2) = 0

⇒ α = 2, 4

So, α can be 2 or 4,

Hence the common root is 2

Answer 2

Answer:

so common root is 2

Step-by-step explanation:

common root is 2

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