If the roots of the equation x2 - bx + c = 0 are α and β, then the equation whose roots are -α and -β will be
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x2 - bx - c = 0
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x2 + bx + c = 0
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x2 + bx - c = 0
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More than one of the above
If roots are alpha and beta, x^2 - bx + c = 0. Sum = alpha+beta = b, Product = alpha*beta = c. New roots are -alpha and -beta. New sum = -(alpha+beta) = -b. New product = (-alpha)*(-beta) = alpha*beta = c. Equation: x^2 - (sum)x + (product) = 0 -> x^2 - (-b)x + c = 0 -> x^2 + bx + c = 0.
For the original equation x^2 - bx + c = 0, the sum of the roots is (alpha + beta) = b and the product of the roots is (alpha * beta) = c. To find the new equation with roots -alpha and -beta, calculate the new sum as -alpha + (-beta) = -(alpha + beta) = -b, and the new product as (-alpha) * (-beta) = alpha * beta = c. A quadratic equation can be formed using x^2 - (sum)x + (product) = 0. Substituting the new sum and product gives x^2 - (-b)x + c = 0, which simplifies to x^2 + bx + c = 0.