Maths-
General
Easy

Question

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

  1. both roots in [a, b]    
  2. both roots in left parenthesis negative straight infinity comma a right parenthesis    
  3. both roots in left square bracket b comma straight infinity right parenthesis    
  4. one root in  left parenthesis negative straight infinity comma a right parenthesis straight & text  other in  end text left parenthesis b comma plus straight infinity right parenthesis  

Hint:

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. Here we have to find the roots of equation, (x - a) (x - b) - 1 if b > a.

The correct answer is: one root in  left parenthesis negative straight infinity comma a right parenthesis straight & text  other in  end text left parenthesis b comma plus straight infinity right parenthesis


    A quadratic equation, or sometimes just quadratics, is a polynomial equation with a maximum degree of two. It takes the following form:
    ax² + bx + c = 0
    where a, b, and c are constant terms and x is the unknown variable.
    Now we have given the equation as: (x - a) (x - b) - 1 = 0. Simplifying it, we get:
    x2(a+b)xab1=0
    Now lets find the discriminant. The formula is:
    D=b2-4ac 
    Applying it, we get:
    D=(a+b)24(ab1)
    D=(ab)2+4
    D>0
    So now we can say that it has two real roots. Also f(a)=1 and f(b)=1 but a which eventually means that a and b are distinct as coefficient of x2 is position (it is 1), minima of f(x) is between a and b.
    Therefore, one of the roots will be in the interval of (α,a) and the other root will be in the interval (b,α).

    Here we used the concept of quadratic equations and solved the problem. We also understood the concept of discriminant and used it in the solution to find the intervals. Therefore, one of the roots will be in the interval of (α,a) and the other root will be in the interval (b,α).

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