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If b>a the the equation (x-a)(x-b)-1=0 ,can both its roots lie between (-infinte,a)?Reason .

If b>a the the equation (x-a)(x-b)-1=0 ,can both its roots lie between (-infinte,a)?Reason .
 

Grade:12

1 Answers

Vikas TU
14149 Points
7 years ago
From the concepts of Locus of Roots,
f(a) = -1
and also
f(b) = -1
both are equal that is f(a) = f(b)
and both are negative and the coeff. of the x^2 in the quadratic is also 1 therefore, the quadratic curve would be upwards.
Hence it is obvious now that a and b lies b/w the roots.
Hence, one root would lie b/w (-infinit,a) and other would be probably into
(b,infinity). 

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