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Find the condition if the roots of a x^2...

Find the condition if the roots of `a x^2+2b x+c=0 and b x^2-2sqrt(a c x)+b=0` are simultaneously real.

Text Solution

Verified by Experts

The correct Answer is:
`b^(2) = ac`
The equations `ax^(2) + 2bx + c = 0 and bx^(2) - sqrt(ac) x + b = 0` have real roots . Therefore,
`4b^(2) - 4acge 0 and 4ac - 4b^(2) ge 0`
`rArr b^(2) = ac`
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