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

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

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

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

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 ?

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 the quadratic equation (b-c)x_2+(c-a)x+(a-)=0 has equal roots, then show that 2b=a+c .

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