If the quadratic equation`4x^2-2(a+c-1)x+a c-b=0(a > b > c)` (a)Both roots se greater than `a` (b)Both roots are less than `c` (c)Both roots lie between `c/2` and `a/2` (d)Exactly one of the roots lies between `c/2` and `a/2`

If a, b, c in R and the quadratic equation x^2 + (a + b) x + c = 0 has no real roots then

The roots of the quadratic equation (a + b-2c)x^2+ (2a-b-c) x + (a-2b + c) = 0 are

Let x^2-(m-3)x+m=0 (m epsilon R) be a quadratic equation . Find the values of m for which the roots are (ix)one root is smaller than 2 & other root is greater than 2 (x) both the roots are greater than 2 (xi) both the roots are smaller than 2 (xii)exactly one root lies in the interval (1;2) (xiii) both the roots lies in the interval (1;2) (xiv) atleast one root lies in the interval (1;2) (xv) one root is greater than 2 and the other root is smaller than 1

Let x^2 - (m - 3) x + m = 0 (m in R) be a quadratic equation, then find the values of 'm' for which both (a) the roots are greater than 2. (b) both roots are positive, ( c) one root is positive and other is negative. ( d) One root is greater than 2 and other smaller than 1 ( e) Roots are equal in magnitude and opposite in sign, ( f) both roots lie in the interval (1, 2)

lf 0 < a < b < c < d , then the quadratic equation ax^2 + [1-a(b+c)]x+abc-d=0 A) Real and distinct roots out of which one lies between c and d B) Real and distinct roots out of which one lies between a and b C) Real and distinct roots out of which one lies between b and c (D) non -real roots

The roots of the equation (b-c) x^2 +(c-a)x+(a-b)=0 are

Let x^2-2(a - 1)x + a - 1 = 0 (a in R) be a quadratic equation, then find the value of 'a' for which (a) Both the roots are positive (b)Both the roots are negative (c) Both the roots are opposite in sign. (d) Both the roots are greater than 1. (e)Both the roots are smaller than 1. (f) One root is small than 1 and the other root is greater than 1.

The quadratic equation, a (x -b)(x-c) + b (x-c)(x-a) + c (x-a) (x-b)=0 , : where 0 ltaltbltc have a) exactly one root lying betwen a and b b) exactly one root lying between b and c C) exactly one root lying between a and c D) both roots lying between a and c

If roots of quadratic equation x ^2 −kx+4=0 then k will be a. 2 b 1 c. 3 d. 4

If both roots of the equation x^2-2ax + a^2-1=0 lie between (-2,2) then a lies in the interval