Home
Class 12
MATHS
If (1-p) is a root of quadratic equation...

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

Text Solution

Verified by Experts

The correct Answer is:
`x = 0, -1`
Since ( 1 - p) is the root of quadration equation
`x^(2) + px + (1 - p) = 0`
So (1 - p) satisfies the above equation. Therefor,
`(1 - p)^(2) + p (1 - p) + (1 - p) = 0`
or `( 1 - p)[1 - p + p + 1] = 0`
or `(1-p) (2) = 0`
or ` p = 1`
On putting this value of p in Eq. (1), we get
`x^(2) + x = 0`
or ` x(x + 1) = 0`
or `x = 0, -1`
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 2.2|5 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 2.3|3 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise SOLVED EXAMPLES|14 Videos

  • STRAIGHT LINES

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

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise All Questions|291 Videos

Similar Questions

Explore conceptually related problems

If one of the roots of the quadratic equation be x^2 - (1+b)x+6 = 0 be 2, then find the other root.

The roots of the quadratic equation 2x^2+3x+1 =0 are

If the roots of a quadratic equation be p+q and p-q, then find the equation.

Find the roots of the quadratic equation |x^(2)|-3|x|+2=0 .

If alphaandbeta be the roots of the quadratic equation 2x^(2)+2x-3=0 , then find the values of alpha+beta+1

Let alpha,beta in Rdot If alpha,beta^2 are the roots of quadratic equation x^2-p x+1=0. a n dalpha^2,beta are the roots of quadratic equation x^2-q x+8=0, then find p ,q,alpha,betadot

IF alpha,beta be the roots of the quadratic equation x^2-px+q=0 , find the equation whose roots are q/(p-alpha) and q/(p-beta) .Accound for the identity of the equation obtained with the given equation.

If alphaandbeta be the roots of the quadratic equation ax^(2)+bx+c=0 , then find the quadratic equation whose roots are ((1)/(alpha)+1)and((1)/(beta)+1) .

If the roote of the quadratic equation x^(2)-p(x-3)-5=0 are equal then one of the values of p is (-5).

If p and q are the roots of the equation x^2+px+q =0, then