Question

if the equation 2(a2+b2)x2 +2(a+b)x+1=0 has no real roots when A not equal to B.

Answer 1

ѳɳ cѳɱpɑʀiɳg witɦ ɑx2 + ɓx + c = 0 wɛ gɛt ɑ = 2(ɑ2 +ɓ2), ɓ = 2(ɑ + ɓ), c = 1 ɗiรcʀiɱiɳɑɳt ѳԲ tɦɛ quɑɗʀɑtic ɛquɑtiѳɳ = ɓ2 – 4ɑc ɦɛɳcɛ ɓ2 – 4ɑc < 0 tɦuร tɦɛ ʀѳѳtร ɑʀɛ iɱɑgiɳɑʀy ѳʀ cѳɱpʆɛx.

Answer 2

Answer:

The given equation is :

To prove:

The given equation has no real roots when a ≠ b .

Solution :

Since for a quadratic equation to have real roots , its discriminant should be positive or equal to zero .

So here :

Or,

Or ,

Or,

Or,

Or,

Since the square of any number can never be less than 0 .

So the only possibility is :

Or,

Or, a= b

Hence , the given equation can have real roots only when a = b .

Step-by-step explanation: