Quadratic EquationHard
Question
If $\alpha$ and $\beta$ are roots of the equation $ax^{2} + bx + c = 0$, then the roots of the equation ${ax}^{2} - bx(x + 1) + c(x + 1)^{2} = 0$ are
Options
A.$\frac{\alpha}{\alpha + 1},\frac{\beta}{\beta + 1}$
B.$\frac{- \alpha}{\alpha + 1},\frac{- \beta}{\beta + 1}$
C.$\frac{\alpha}{1 - \alpha},\frac{\beta}{1 - \beta}$
D.$\frac{\alpha}{\alpha - 1},\frac{\beta}{\beta - 1}$
Solution
$a\left( \frac{- x}{x + 1} \right)^{2} + b\left( \frac{- x}{x + 1} \right) + c = 0$
$$\Rightarrow \ \frac{- x}{x + 1} = \alpha,\beta \Rightarrow x = \frac{- \alpha}{\alpha + 1},\frac{- \beta}{\beta + 1}$$
Create a free account to view solution
View Solution FreeMore Quadratic Equation Questions
If x1, x2, .........xn are any real numbers and n is any positive integer, then...Three real numbers $x,y,z$ are such that $x^{2} + 6y = - 17,y^{2} + 4z = 1$ and $z^{2} + 2x = 2$. Then the value of $x^{...The number of real solutions of the equation is -The number of real solutions of the equation = − 3 + x − x2...If α, β be the roots of x2 + px - q = 0 and γ, δ be the roots of x2 + px + r = 0, q + r ≠ 0 th...For what value of a, the difference of roots of the equation (a−2) x2 − (a − 4) x − 2 = 0 is equ...