Question

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 the common root is
[AIEEE-2008]
(A)1
(B)4
(C)3
(D) 2​

Answer 1

Answer:it's d . a= 2

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

(refer image 1)

For x2 – cx + 6 = 0

(refer image 1)

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

(refer image 2)

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:

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