For what range of values of x is x\(^2\) - 2x - 3... | WAEC SSCE - Further Mathematics - 2021 (Objective)

Question 1 Report

For what range of values of x is x\(^2\) - 2x - 3 ≤ 0

{x: -1 ≤ x ≤ 3}

{ x: -3 ≤ x ≤ 1}

{ x: -3 ≤ x ≤ -1}

{ x: 1 ≤ x ≤ 3}

Answer Details

To solve the inequality x\(^2\) - 2x - 3 ≤ 0, we can use factoring or the quadratic formula. Factoring gives us (x - 3)(x + 1) ≤ 0, which means that the expression is less than or equal to zero when x is between or equal to -1 and 3, since the factors change sign at these values. Therefore, the correct answer is {x: -1 ≤ x ≤ 3}. Alternatively, we can use the quadratic formula to find the roots of the equation x\(^2\) - 2x - 3 = 0, which are x = -1 and x = 3. Since the quadratic function is a parabola that opens upward, it is negative in the interval between these two roots. Therefore, the expression x\(^2\) - 2x - 3 is less than or equal to zero when x is between or equal to -1 and 3.

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Polynomial Functions

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For what range of values of x is x\(^2\) - 2x - 3 ≤ 0

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