GCE Mathematics 2022 Objective — Question 47
Question 47 of 50 from the General Certificate of Education (GCE) Mathematics 2022 Objective paper, with the correct answer and a full explanation.
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If the equations x^2-5x+6=0 and x^2+px+6=0 have a common root, find the value of p.
- A. 5
- B. 6
- C. -6
- D. -5Correct
Explanation
x^2-5x+6=0 factorizes as (x-2)(x-3)=0, giving roots x=2 or x=3. Comparing x^2+px+6=0 with x^2-5x+6, p=-5 (the equations are identical when p=-5).
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