Maths-
General
Easy

Question

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

Hint:

## The correct answer is: one root in

### 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 = 0where 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)x−ab−1=0Now lets find the discriminant. The formula is:D=b2-4ac it has two real roots. Also  and  but  which eventually means that  and  are distinct as coefficient of  is position (it is ), minima of  is between  and Therefore, one of the roots will be in the interval of  and the other root will be in the interval .

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  and the other root will be in the interval .