Question

Which of the following quadratic equations has roots 2, -1 ?
(A) x² + x + 2 = 0
(B) x? -x- 2 = 0
(C) x2 + 2x - 2 = 0
D) x2-2X+2=0​

Answer 1

Answer:

option B is correct answer

Answer 2

Given:

A quadratic equation has roots -1 and 2.

To Find:

The equation of the polynomial.

Solution:

The given problem can be solved using the concepts of quadratic equations.

1. Consider a quadratic equation with roots a and b.

=> The equation of the quadratic form with the roots a and b is given by the formula: x² - (a+b)x + ab = 0.

2. Using the formula above, the quadratic equation can be found,

=> Quadratic equation = x² - (a+b)x + ab = 0,

=> Quadratic equation = x² - (2+(-1))x + (2)(-1) = 0,

=> Quadratic equation = x² - (2-1)x + (-2) = 0,

=> Quadratic equation = x² - (1)x -2 = 0,

=> Quadratic equation = x² -x -2 = 0.

3. The quadratic equation is x² -x -2 = 0.

Therefore, the equation of the quadratic form is x² -x -2 = 0. Option B is the correct answer.