Multiple choice

Roots of the equation $2{x}^{2}-5x+1=0$, ${x}^{2}+5x+2=0$ are

  1. reciprocal and of same sign

  2. reciprocal and of opposite sign

  3. equal in product

  4. None of these
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A Correct answer
AI explanation

Let the roots of the first equation 2x^2-5x+1=0 be alpha and beta, so their product alpha*beta is c/a = 1/2. The second equation x^2+5x+2=0 has a product of roots equal to 2. Since the product of the roots of the second equation is the reciprocal of the product of the first, the sets of roots are reciprocals of each other. Both equations have a negative sum and positive product, meaning all roots are negative, so they share the same sign.

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