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Find the roots of the equation if the roots of the quadratic equation 7m2 – 14m + a = 0 are reciprocal to each other.
  • a)
    1, 1
  • b)
    1, 7
  • c)
    1, 14
  • d)
    7, 7
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Find the roots of the equation if the roots of the quadratic equation ...
We know if ax2 + bx + c = 0 is a quadratic equation, product of the roots = (c/a)
⇒ In the given problem a = 7, b = -14, c = a
If the roots of the equation are reciprocal to each other, then the product of the roots = 1
⇒ (a/7) = 1
⇒ a = 7
On putting ‘a’ = 7 in the original equation, the equation will now be 7m2 – 14m + 7 = 0
⇒ m2 – 2m + 1 = 0 (Dividing the previous equation with 7 on both sides)
⇒ m2 – m – m + 1 = 0
⇒ m (m – 1) – (m -1) = 0
⇒ (m - 1) (m – 1) = 0
⇒ (m - 1)2 = 0
⇒ m = 1
∴ So, the roots of the quadratic equation are 1, 1
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Find the roots of the equation if the roots of the quadratic equation 7m2– 14m + a = 0 are reciprocal to each other.a)1, 1b)1, 7c)1, 14d)7, 7Correct answer is option 'A'. Can you explain this answer?
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