show that the equation 2(a2+b2)x2+2(a+b)x+1=0 has no real roots,when a is not= to b - Maths - Equations and Inequations

Question

show that the equation
2(a2+b2)x2+2(a+b)x+1=0 has no real
roots,when a is not= to b

Anuradha Sharma · Accepted Answer

The given equation is, 2a2+b2x2+2a+bx+1=0Comparing it with Ax2+Bx+C=0 we get, A=2a2+b2, B=2a+b, C=1Now calculating D=B2-4AC=2a+b2-4×2a2+b2=4a2+4b2+8ab-8a2-8b2=-4a2-4b2+8ab=-4a2+4b2-8ab=-4a2+b2-2ab=-4a-b2Since squared quantity is always positive hence a-b2≥0Now it is given a≠b, so a-b2>0So D=-4 a-b2 will be negative
Hence the equation has no real roots

show that the equation 2(a2+b2)x2+2(a+b)x+1=0 has no real roots,when a is not= to b.

show that the equation 2(a²+b²)x²+2(a+b)x+1=0 has no real roots,when a is not= to b.