This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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You're on a roll — This question has two parts. Let's solve them one by one. Question 8 (a)(i): For what value(s) of x is the expression (x^2 + 15x + 50)/(x-5) not defined? Step 1: An algebraic expression with a fraction is undefined when its denominator is equal to zero. Set the denominator to zero: x - 5 = 0 Step 2: Solve for x. x = 5 The expression is not defined when x = 5. Question 8 (a)(ii): Find the value(s) of x for which the expression is zero. Step 1: An algebraic expression with a fraction is zero when its numerator is equal to zero, provided the denominator is not zero for those values of x. Set the numerator to zero: x^2 + 15x + 50 = 0 Step 2: Factorize the quadratic equation. We need two numbers that multiply to 50 and add to 15. These numbers are 5 and 10. x^2 + 5x + 10x + 50 = 0 Step 3: Factor by grouping. x(x+5) + 10(x+5) = 0 (x+5)(x+10) = 0 Step 4: Set each factor to zero and solve for x. x+5 = 0 x = -5 x+10 = 0 x = -10 Step 5: Check if these values make the denominator zero. For x = -5, the denominator is -5 - 5 = -10 ≠ 0. For x = -10, the denominator is -10 - 5 = -15 ≠ 0. Since neither value makes the denominator zero, both are valid solutions. The values of x for which the expression is zero are -5 and -10. Drop the next question 📸