. Form a quadratic equation in the form ax²+bx+c=0 whose roots are b and twice the negative reciprocal of b. (3mk)
(x-b)(x+2/b)
x^2+2x/b -bx -2
x^2 +(2/b -b)x -2
To form a quadratic equation with the given roots, we need to know that the sum and product of the roots of a quadratic equation are related to its coefficients. For a quadratic equation in the form ax^2 + bx + c = 0 with roots α and β, the sum of the roots is given by α + β = -b/a, and the product of the roots is given by α * β = c/a.
Let's denote the first root b and the second root as twice the negative reciprocal of b, which can be written as -2/b.
Since the sum of the roots is given by α + β = -b/a, we have:
b + (-2/b) = -b/a
Multiply both sides by b to clear the fraction:
b^2 - 2 = -ab
Rearrange the equation to get the quadratic equation in the desired form:
ab + b^2 - 2 = 0
So, the quadratic equation in the form ax^2 + bx + c = 0 with roots b and twice the negative reciprocal of b is:
ab + b^2 - 2 = 0
Please note that we do not have the values of a, b, or c, so the equation is given in terms of those variables.