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Number of values of x satisfying the pai...

Number of values of `x` satisfying the pair of quadratic equations `x^(2)-px+20=0` and `x^(2)-20x+p=0` for some `p in R` is

A

A. `0`

B

B. `1`

C

C. `2`

D

D. `3`

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)` Given equations are
`x^(2)-px+20=0`
`x^(2)-20x+p=0`
If `p=20` both the quadratic equations are identical hence `x=10+4sqrt(5)` or `x=10-4sqrt(5)`
If `p ne 20`, then subtracting equations, we get
`(20-p)x+(20-p)=0`
`implies x=-1`
Hence there are `3` values f `x`
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