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Common Roots

29. If b>a, t...

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29. If b>a, then the equation (x-a)(x-b)-1=0 has Option.1) Both roots in [a,b] Option.2)Both roots in (-infinty,a) Option.3)Both roots in (b,+infinity) Option.4)One root in (-infinity,a) and other in (b,+infinity)

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Q. If b > a. then the equation (x-a) (x-b) -1 = 0 has:

x^{2} - a x + b = 0

a, b \in R

be a quadratic equation such that the roots are opposite in sign and the magnitude of one root is twice the other. Then which of the following options is/are always true ?

x^{2} - a x + b = 0

a, b \in R

be a quadratic equation such that the roots are opposite in sign and the magnitude of one root is twice the other. Then which of the following options is/are always true ?

a, b (b > a)

are the roots of the quadratic equation

(k + 1) x^{2} - (20 k + 14) x + 91 k + 40 = 0;

k > 0

, then which among the following option(s) is/are correct for the roots

a, b \in R, a \neq 0

and the quadratic equation

a x^{2} - b x + 1 = 0

has imaginary roots, then

(a + b + 1)

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