Home
Class 12
MATHS
Let x^2-3x+p=0 has two positive roots aa...

Let `x^2-3x+p=0` has two positive roots `aa n db` , then minimum value if `(4/a+1/b)` is,

Text Solution

Verified by Experts

The correct Answer is:
3
a + b = 3
H.M `ge` A.M for numbe `(a)/(2), (a)/(2)`, b. We have
`(3)/((2)/(a) + (2)/(a) + (1)/(b)) le ((a)/(2) + (a)/(2) + 6)/(3) = 1`
`:. 1 ge (3)/((2)/(a) + (2)/(a) + (1)/(b))`or `(2)/(a) + (2)/(a) + (1)/(b) ge 3`
`:. (4)/(a) + (1)/(b) ge 3`
Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE PUBLICATION|Exercise Jee Advanced (Single|1 Videos

  • INEQUALITIES INVOLVING MEANS

    CENGAGE PUBLICATION|Exercise Linked comprehension type|6 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE PUBLICATION|Exercise Single correct Answer|21 Videos

  • INTEGRALS

    CENGAGE PUBLICATION|Exercise All Questions|762 Videos

Similar Questions

Explore conceptually related problems

If x^2-(a-3)x+a =0 has at least one positive root,then

If x^(2) +ax - 3x-(a+2) = 0 has real and distinct roots, then minimum value of (a^(2)+1)/(a^(2)+2) is

If the cubic 2x^3-9x^2+12 x+k=0 has two equal roots then minimum value of |k| is______.

If x^2+3x+5=0a n da x^2+b x+c=0 have common root/roots and a ,b ,c in N , then find the minimum value of a+b+ c dot

The number of values of k for which the equation x^(2)-3x+k=0 has two distinct roots lying in the interval ( 0 , 1 ) are

If l ,m ,n are the three positive roots of the equation x^3-a x^2+b x-48=0, then the minimum value of (1//l)+(2//m)+(3//n) equals a 1 b 2 c 3/2 d 5/2

Let x and y be two variables and x gt 0, xy=1, then the minimum value of (x+y) is-

If equations x^2+a x+12=0. x^2+b x+15=0a n dx^2+(a+b)x+36=0, have a common positive root, then find the values of a a n d bdot

If the roots of the cubic equation, x^3+a x^2+b x+c=0 are three consecutive positive integers, then the value of (a^2//(b+1)) is equal to?

Let x and y be two variables and x gt 0 , xy=1 , then the minimum value of x+y is-