Home
Class 9
MATHS
If one of the roots of x^2+(1+k)x+2k=0 i...

If one of the roots of `x^2+(1+k)x+2k=0` is twice the other, then `(a^2+b^2)/(ab)=`

A

2

B

1

C

4

D

7

Text Solution

Verified by Experts

The correct Answer is:
D
(i) Use of the concept of sum and product of the roots of a quadratic equation.
(ii) Assume the roots as `alpha` and `2alpha`.
(iii) Find the sum of the roots and product of the roots.
(iv) From the above equation eliminate `'alpha'` .
(v) Then obtain the value of `(k^(2) + 1)/(k)`.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • QUADRATIC EXPRESSIONS AND EQUATIONS

    PEARSON IIT JEE FOUNDATION|Exercise Level 3|23 Videos

  • QUADRATIC EXPRESSIONS AND EQUATIONS

    PEARSON IIT JEE FOUNDATION|Exercise Level 1|30 Videos

  • PROBABILITY

    PEARSON IIT JEE FOUNDATION|Exercise LEVEL 3|8 Videos

  • RATIO, PROPORTION AND VARIATION

    PEARSON IIT JEE FOUNDATION|Exercise Leval 3|10 Videos

Similar Questions

Explore conceptually related problems

If one root of the equation 8x^(2)-6x+k=0 is the square of the other,then k=

If one root of x^(3)+2x^(2)+3x+k=0 is the sum of the other two roots then k=

Knowledge Check

  • If one root of x^(2) - x - k = 0 is square of the other, then k =

    A
    `2 pm sqrt5`
    B
    `2 pm sqrt3`
    C
    `3 pm sqrt2`
    D
    `5 pm sqrt2`

  • If one root of 5x^(2)+13x +k=0 is reciprocal of the other, then

    A
    k=0
    B
    k=5
    C
    k=1/6
    D
    k=6

  • If one root of x^(2)-x-k=0 be square of the other, then k is equal to

    A
    `2 pm sqrt(3)`
    B
    `3 pm sqrt(2)`
    C
    `2 pm sqrt(5)`
    D
    `5 pm sqrt(2)`

    • Similar Questions

    Explore conceptually related problems

    If one zero of the polynomial 2x^(2)-5x-(2k+1) is twice the other,then find both the zeroes of the polynomial and the value of k

    If one root of (a ^(2) – 5a + 3) x ^(2) + ( 3a -1) x + 2 =0 is twice the other, then what is the value of ‘a’ ?

    If slope of one of the lines ax^(2)+2hxy+by^(2)=0 is k times slope of the other, then ab(1+k)^(2)=

    The value of 'k' for which one of the roots of x^(2) - x + 3 k = 0 , is double of one of the roots of x^(2) - x + k = 0 , is

    If one root of the equation 8x^(2)-6x-k-3=0 is the square of the other, then the values of k are

    Home
    Profile