Home
Class 12
MATHS
A quadratic equations p(x)=0 having coef...

A quadratic equations `p(x)=0` having coefficient `x^(2)` unity is such that `p(x)=0` and `p(p(p(x)))=0` have a common root, then

A

`p(0) p(1) gt 0`

B

`p(0) p(1) lt 0`

C

`p(0) p(1) = 0`

D

`p(0)=0` and `p(1)=0`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` let `p(x)=x^(2)+ax+b` and let `alpha` be the common root
`:. P(alpha)=0` and `p(p(p(alpha)))=0impliesp(p(0))=0`
`implies p(alpha)=0`
Now `p(0)=b`
`:. P(b)=0` ,brgt `implies b^(2)+ab+b=0`
`implies b(b+a+1)=0`
`implies p(0)p(1)=0`
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE ENGLISH|Exercise Comprehension|12 Videos

  • THEORY OF EQUATIONS

    CENGAGE ENGLISH|Exercise Multiple Correct Answer|6 Videos

  • STRAIGHT LINES

    CENGAGE ENGLISH|Exercise ARCHIVES (NUMERICAL VALUE TYPE)|1 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise All Questions|294 Videos

Similar Questions

Explore conceptually related problems

The quadratic equation p(x)=0 with real coefficients has purely imaginary roots. Then the equation p(p(x))=0 has A. only purely imaginary roots B. all real roots C. two real and purely imaginary roots D. neither real nor purely imaginary roots

If p(x)=4x-6 and p(a)=0 , then a=

If the equadratic equation 4x ^(2) -2x -m =0 and 4p (q-r) x ^(2) -2p (r-p) x+r (p-q)-=0 have a common root such that second equation has equal roots then the vlaue of m will be :

If the equadratic equation 4x ^(2) -2x -m =0 and 4p (q-r) x ^(2) -2p (r-p) x+r (p-q)-=0 have a common root such that second equation has equal roots then the vlaue of m will be :

If x^(2)+px+q=0 and x^(2)+qx+p=0 have a common root, prove that either p=q or 1+p+q=0 .

Find the vaues of p if the equations 3x^2-2x+p=0 and 6x^2-17x+12=0 have a common root.

A quadratic trinomial P(x)=a x^2+b x+c is such that the equation P(x)=x has no real roots. Prove that in this case equation P(P(x))=x has no real roots either.

A quadratic trinomial P(x)=a x^2+b x+c is such that the equation P(x)=x has o real roots. Prove that in this case equation P(P(x))=x has no real roots either.

If (1-p) is a root of quadratic equation x^2+p x+(1-p)=0, then find its roots.

If (1-p) is a root of quadratic equation x^2+p x+(1-p)=0, then find its roots.