Statement (1): The equation `(x – a) (x – c) + lambda (x – b) (x – d) = 0` where `a < b < c < d` has non real roots if `lambda > 0.`Statement (2): The equation `(a, b, c in R) ax^2 + bx+c=0` has non real roots if `b^2-4ac <0 .`

If a

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

Statement -1 : The quadratic equation ax^(2)+bx+c=0 has real roots if (a+c)^(2) gt b^(2) , AA , a,b,c in R . and Statement -2 : The quadratic equation ax^(2) +bx+c=0 has real roots if b^(2) -4ac ge 0

If the equation ax^(2)+bx+c=0 has non-real roots,prove that 1+(c)/(a)+(b)/(a)>0

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

Statement-1 : The equation x^(2)-2009x+2008 =0 has rational roots . and Statement -2 : The quadratic equation ax^(2)+bx+c=0 has rational roots iff b^(2)-4ac is a prefect square.

Statement-1 : The equation x^(2)-2009x+2008 =0 has rational roots . and Statement -2 : The quadratic equation ax^(2)+bx+c=0 has rational roots iff b^(2)-4ac is a prefect square.

Study the statement carefully. Statement I : Both the roots of the equation x^(2) - x + 1 = 0 are real. Statement II : The roots of the equations ax^(2) + bx + c = 0 are real if and only b^(2) - 4ac gt 0 . Which of the following options hold?

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