Home
Class 12
MATHS
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

`0`

B

`1`

C

`2`

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`
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Multiple Correct Answer|6 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Comprehension|12 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise JEE Advanced Previous Year|4 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Question Bank|20 Videos

Similar Questions

Explore conceptually related problems

Solve each of the following quadratic equations: 100x^(2)-20x+1=0

The value of p for which the quadratic equation 4x^(2)+px+3=0 has equal roots are.

Find the value of p for which the quadratic equation 4x^2+px+3=0 has equal roots

For p=____ the quadratic equation 9x^(2)-3px+p=0 has equal roots.

If the equations x^(2)-x-p=0 and x^(2)+2px-12=0 have a common root,then that root is

The value of p for which both roots of the quadratic equation 2x^(2)-2(1+2p)x+p(1+p)=0 ( p in R ) are smaller than 2 is

For what values of p the quadratic equation 3x^(2) + 12x + 4p = 0 has equal roots?

Find the value of p for which the quadratic equation x^(2)+p(4x+p-1)+2=0 has equal roots :