Multiple choice

Roots of quadratic equation $21x\,=\,196\,-\,x^{2}$ are

  1. $-28, 7$
  2. $- 28, -7$
  3. $28,- 7$

  4. None of these
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A Correct answer
Explanation

Rearranging the equation: x^2 + 21x - 196 = 0. Using the quadratic formula or factoring: (x + 28)(x - 7) = 0. The roots are -28 and 7.

AI explanation

First, rewrite the given equation 21x equals 196 minus x squared into standard form as x squared plus 21x minus 196 equals 0. Using the method of splitting the middle term, we find two numbers that multiply to minus 196 and add to 21, which are 28 and minus 7. This allows us to factor the equation as x minus 7 times x plus 28 equals 0. Setting each factor to zero gives the roots as 7 and minus 28.

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