Home
Class 12
MATHS
If both the roots of the quadratic equat...

If both the roots of the quadratic equation `x^(2) -mx+4=0` are real and distinct and they lie in the interval `[1,5]` then m lies in the interval

A

`(4,5)`

B

`(-5,-4)`

C

`(5,6)`

D

`(3,4)`

Text Solution

Verified by Experts

The correct Answer is:
A
According to given information, we have the following graph

Now, the folowing conditions should satisfy
`(i) Dgt0impliesb^(2)-4ac gt0`
`impliesm^(2)-4xx1xx4gt0`
`implies m^(2)-16gt0`
`implies(m-4)(m+4)gt0`
`impliesm in (-oo,-4)uu(4,oo)`
(ii) The value of the parabola should lie between `x=1and x=5`
`therefore-(b)/(2a)in(1,5)impliesltm/2lt5impliesm in (2,10)`
(iii) `f(I)gt0implies1-m+4 gt 0`
`impliesmlt5impliesm in (-oo,5)`
(iv) `f(5)gt0implies25-5m+4gt0implies5mlt29impliesm in(-oo,(29)/(5))`
From the values of m obtained in (i),(ii),(iii),and (iv), we get `m in (4,5).`
Promotional Banner

Similar Questions

Explore conceptually related problems

The real roots of the quadratic equation x^(2)-x-1=0 are ___.

If the both the roots of the quadratic equation x^(2)-2kx+k^(2)+k-5=0 are less than 5, then k

If the roots of the quadratic equation 3x^(2)+2x+a^(2)-a=0 in x are of opposite signs, then a lies in the interval

If the equation x^4- λx^2+9=0 has four real and distinct roots, then lamda lies in the interval

If the roots of the equation x^2+2a x+b=0 are real and distinct and they differ by at most 2m ,then b lies in the interval a. (a^2,a^2+m^2) b. (a^2-m^2, a^2) c. [a^2-m^2, a) d. none of these

If the equation has no real root, then lamda lies in the interval

if the roots of the quadratic equation (4p - p^(2) - 5)x^(2) -(2p−1)x+3p=0 are greater then - 2 less then 4 then p lie in the interval

If the roots of the equation x^2-8x+a^2-6a=0 are real and distinct, then find all possible value of adot

If |2x-3| lt |x+5| , then x lies in the interval