Question

If one of the roots of the equation x² + ax - b = 0 is 1, then what is the value of (a - b)?
1. -1
2. 1
3. 2
4. -2
5. None of these

Answer 1

Correct Answer - Option 1 : -1

CONCEPT:

The values of variable satisfying the given quadratic equation are called the roots of that quadratic equation.

i.e If x = α is a root of the equation f(x) = 0 then f(α) = 0

CALCULATION:

Given: One of the roots of the equation x2 + ax - b = 0 is 1.

Here, we have to find the value of a - b.

As we know that, if x = α is a root of the equation f(x) = 0 then f(α) = 0

∵ x = 1 is the root of the equation f(x) = x2 + ax - b = 0 i.e f(1) = 0

By substituting x = 1 in the equation x2 + ax - b = 0, we get

⇒ 1² + a × 1 - b = 0

⇒ a - b = - 1

Hence, option A is the correct answer.