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A straight line y = mx meets the curve y = x2 – 12x +…

A straight line y = mx meets the curve y = x2 – 12x + 40 in two distinct points. If one of them is (5, 5) find the other

  • A.
    (5, 6)
  • B.
    (8, 8)
  • C.
    (8, 5)
  • D.
    (7,7)
  • E.
    (7, 5)
Correct Answer: Option E
Explanation

When y = 5, y = x2 – 12x + 40, becomes
x2 – 12x + 40 = 5
x2 – 12x + 40 – 5 = 0
x2 + 12x + 35 = 0
x2 – 7x – 5x + 35 = 0
x(x – 7) – 5(x – 7) = 0
= (x – 5)(x – 7)
x = 5 or 7