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`

In the quadratic equation 4x^(2) - 2 ( a + c - 1) x + ac - b = 0 (a gt b gt c)

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

for what values of m, the equation 2x^(2) -2 ( 2m +1) x+ m ( m +1) = 0 m in R has (i) Both roots smallar than 2 ? (ii) Both roots greater than 2 ? (iii) Both roots lie in the interval (2,3) ? (iv) Exactly one root lie in the interval (2,3) ? (v) One root is smaller than 1, and the other root is greater than 1 ? (vi) One root is greater than 3 and the other root is smaller than 2 ? (vii) Roots alpha and beta are such that both 2 and 3 lie between alpha and beta ?

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 equation (b-c)x^(2)+(c-a)x+(a-b)=0

Let x^2-(m-3)x+m=0 (mepsilonR) 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

For a quadratic equation ax^2+bx+c state the condition when: (i) Both the roots are greater than a given number k.. (ii)Both the roots will be less than a given number k.. (iii)Both the roots will lie on the given interval(k_1,k_2).. (iv) Exactly one of the roots lie in the interval(k_1,k_2)... (v)A given number k will lie between the roots..

If the roots of the quadratic equation (a-b) x^(2) + (b - c) x + (c - a) =0 are equal , prove that b +c = 2a

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