If b(1)b(2)= 2(c(1)+c(2)), then prove th...

If `b_(1)b_(2)= 2(c_(1)+c_(2))`, then prove that at least one of the equations `x^(2) +b_(1)x+c_(1)=0 and x^(2) +b_(2)x+ c_(2)=0` has real roots.

Similar Questions

Explore conceptually related problems

If the roots of the equation x ^(2) + 2 bx + c =0 are alpha and beta, then b ^(2) - c is equal to

If the roots of the equation (x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0 are equal, then a^(2)+b^(2)+c^(2) is equal to

The quadratic equation (x-a) (x-b)+ (x-b)(x-c) + (x-c) (x-a) =0 has equal roots, if

The number of real roots of the equation |x|^(2) - 3|x| + 2 = 0 is a)1 b)2 c)3 d)4

Given that the equation x ^(2) - (2a + b ) x + (2a ^(2) + b ^(2) - b + (1)/(2)) = 0 has two real roots. The value of a and b is

If the roots of the equation x^(2) - bx + c = 0 are two consecutive integers, then b^(2) - 4c is