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

Show that the roots of the quadratic equation: (b - c)x^(2) + (c - a) x + (a - b) = 0 are equal if c + a = 2b.

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

The roots of the quadratic equation ax^(2) + bx + c = 0 (a ! = 0 ) are given x = (-b pm sqrt(b^(2) - 4ac))/(2a) are (i) real and distinct roots if D gt 0 (ii) repeated roots if D = 0 no real roots if D lt 0 , where D = b^(2) - 4ac The nature of the roots of quadratic equation 4x^(2) + 20x + 25 = 0 is

In a quadratic equation ax^(2) + bx + c = 0 "if" b^(2) - 4ac gt 0 then their roots are ….

If a,b,c are rational numbers (a gt b gt c gt 0) and quadratic equation (a+b-2c) x ^(2) + (b+c-2a) x+ (c+a-2b)=0 has a root in the interval (-1,0) then which of the following statement (s) is/are correct ?

If a,b,c are rational numbers (a gt b gt c gt 0) and quadratic equation (a+b-2c) x ^(2) + (b+c-2a) x+ (c+a-2b)=0 has a root in the interval (-1,0) then which of the following statement (s) is/are correct ?