Home
Class 12
MATHS
The equation x^(2)+bx+c=0 has distinct r...

The equation `x^(2)+bx+c=0` has distinct roots. If `2` is subtracted from each root the result are the reciprocal of the original roots, then `b^(2)+c^(2)` is

A

`2`

B

`3`

C

`4`

D

`5`

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)` Let `r_(1)`, `r_(2)` be the roots, from given condition
`r-2=(1)/®impliesr^(2)-2r-1=0`, `b=-2`, `c=-1`, `b^(2)+c^(2)=5`
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Comprehension|12 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Multiple Correct Answer|6 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise JEE Advanced Previous Year|4 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Question Bank|12 Videos

Similar Questions

Explore conceptually related problems

If one root of the equation is the reciprocal of the other root in ax^(2) + bx + c = 0 then ……… .

If the equation x^2-3p x+2q=0a n dx^2-3a x+2b=0 have a common roots and the other roots of the second equation is the reciprocal of the other roots of the first, then (2-2b)^2 . a. 36p a(q-b)^2 b. 18p a(q-b)^2 c. 36b q(p-a)^2 d. 18b q(p-a)^2

If the roots of the equation x^(2)-bx+c=0 are two consecutive integers, then b^(2)-4c is

If the sum of the roots of the quadratic equation ax^(2) + bx + c = 0 is equal to the sum of the squares of their reciprocals, then prove that 2a^(2)c = c^(2)b + B^(2)a.

If the sum of the roots of the quadratic equation ax^2 + bx + c = 0 ( abc ne 0) is equal to the sum of the squares of their reciprocals, the sum of the squares of their reciprocals, then a/c , b/a , c/b are in H.P.

the quadratic equation 3ax^2 +2bx+c=0 has atleast one root between 0 and 1, if

Consider quadratic equations x^2-ax+b=0 and x^2+px+q=0 If the above equations have one common root and the other roots are reciprocals of each other, then (q-b)^2 equals

If the equation ax^2 + bx + c = 0 ( a gt 0) has two roots alpha and beta such that alpha 2 , then

if ax^2+bx+c = 0 has imaginary roots and a+c lt b then prove that 4a+c lt 2b