With b = -1 and c = 0 satisfies Vieta's formulas: the sum of the roots is -b, and the product of the roots is equal to the constant term. Here option C is correct.
Let's consider the quadratic equation x^2 + bx + c = 0 with roots b and c. According to Vieta's formulas:
The sum of the roots (b + c) is equal to the negation of the coefficient of x (with the opposite sign).
The product of the roots (bc) is equal to the constant term.
Now, let's analyze the options:
A) b = 1, c = 0
Sum of the roots: 1 + 0 = 1
Product of the roots: 1 * 0 = 0
The sum is not equal to -b, so this option is not correct.
B) b = 0, c = 1
Sum of the roots: 0 + 1 = 1
Product of the roots: 0 * 1 = 0
The sum is not equal to -b, so this option is not correct.
C) b = -1, c = 0
Sum of the roots: -1 + 0 = -1
Product of the roots: -1 * 0 = 0
The sum is equal to -b, so this option is correct.
D) b = 0, c = -1
Sum of the roots: 0 + (-1) = -1
Product of the roots: 0 * (-1) = 0
The sum is equal to -b, so this option is also correct.
Therefore, both options C and D satisfy the conditions, but only option C has c ≠ 0. Here option C is correct.
Complete question:
The coefficients b and c in the equation x^2 + bx + c = 0 are also the roots of the equation c doesnt equal o find b and c
A) b = 1, c = 0
B) b = 0, c = 1
C) b = -1, c = 0
D) b = 0, c = -1