If b1b2 = 2(c1 + c2) and b1, b2, c1, c2 are all real numbers, then at least one of the equations x2 + b1x + c1 = 0 and x2 + b2x + c2 = 0 has

Question

If b1b2 = 2(c1 + c2) and b1, b2, c1, c2 are all real numbers, then at least one of the equations x2 + b1x + c1 = 0 and x2 + b2x + c2 = 0 has (A) real roots (B) purely imaginary roots (C) roots of the form a + ib (a, b ∈ R , ab ≠ 0) (D) rational roots

Tardigrade Admin · Accepted Answer

We have equations and Now, x2+b1 x+c1=0 D1=b12-4 c1 and x2+b2 x+c2=0 D2=b22-4 c2 Now, D1 + D2=b12+b22-4(c1+c2) =b12+b22-2 b1 b2 [∵ b1 b2=2(c1+c2)] =(b1-b2)2 ≥ 0 ⇒ At least one of D1 and D2 are non-negative real roots.

Q. If $b_{1} b_{2} = 2 (c_{1} + c_{2})$ and $b_{1}, b_{2}, c_{1}, c_{2}$ are all real numbers, then 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

purely imaginary roots

roots of the form $a + ib (a, b \in R, ab \neq = 0)$

rational roots

Q. If b1​b2​=2(c1​+c2​) and b1​,b2​,c1​,c2​ are all real numbers, then at least one of the equations x2+b1​x+c1​=0 and x2+b2​x+c2​=0 has

real roots

purely imaginary roots

roots of the form a+ib(a,b∈R,ab=0)

rational roots

Q. If $b_{1} b_{2} = 2 (c_{1} + c_{2})$ and $b_{1}, b_{2}, c_{1}, c_{2}$ are all real numbers, then at least one of the equations $x^{2} + b_{1} x + c_{1} = 0$ and $x^{2} + b_{2} x + c_{2} = 0$ has

roots of the form $a + ib (a, b \in R, ab \neq = 0)$