The set of values of α for which the quadratic equation (α+2) x2-2 α x-α=0 has two roots on the number line symmetrically placed about the point 1 is

Question

The set of values of α for which the quadratic equation (α+2) x2-2 α x-α=0 has two roots on the number line symmetrically placed about the point 1 is (A)  -1,0  (B)  0,2  (C) φ (D)  0,1

Tardigrade Admin · Accepted Answer

Let roots of the equation be 1-k and 1+k, where k >0 Then 2=(1-k)+(1+k)=(2 α/α+2) ⇒ 1=(α/α+2) This is not possible for any value of α.

Q. The set of values of $α$ for which the quadratic equation $(α + 2) x^{2} - 2 αx - α = 0$ has two roots on the number line symmetrically placed about the point 1 is

${- 1, 0}$

${0, 2}$

$ϕ$

${0, 1}$

Let roots of the equation be
$1 - k$ and $1 + k$ , where $k > 0$
Then $2 = (1 - k) + (1 + k) = \frac{2 α}{α + 2} \Rightarrow 1 = \frac{α}{α + 2}$
This is not possible for any value of $α$ .

Q. The set of values of α for which the quadratic equation (α+2)x2−2αx−α=0 has two roots on the number line symmetrically placed about the point 1 is

{−1,0}

{0,2}

ϕ

{0,1}

Let roots of the equation be 1−k and 1+k, where k>0 Then 2=(1−k)+(1+k)=α+22α​⇒1=α+2α​ This is not possible for any value of α.

Q. The set of values of $α$ for which the quadratic equation $(α + 2) x^{2} - 2 αx - α = 0$ has two roots on the number line symmetrically placed about the point 1 is

${- 1, 0}$

${0, 2}$

$ϕ$

${0, 1}$

Let roots of the equation be
$1 - k$ and $1 + k$ , where $k > 0$
Then $2 = (1 - k) + (1 + k) = \frac{2 α}{α + 2} \Rightarrow 1 = \frac{α}{α + 2}$
This is not possible for any value of $α$ .