Advanced MathHardProduct of the x-coordinates where a line meets a parabola
Advanced Math practice question
In the xy-plane, the graphs of y = x² − 6x + 8 and y = 2x − 7 meet at two points whose x-coordinates are p and q. What is the value of pq?
Answer: 15
x² − 6x + 8 = 2x − 7 gives x² − 8x + 15 = (x − 3)(x − 5) = 0, so pq = 3 × 5 = 15.
Common wrong answers
- If you answered 1
- 1 subtracts 7 from 8, comparing the constants only.
- If you answered 8
- 8 is p + q.
- If you answered -15
- −15 has the sign wrong; both roots are positive.
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