Question

if ax^2+ 2 X + a =0 has two distinct real roots then find the value of a​

Answer 1

Step-by-step explanation:

Given quadratic equation is:

$a {x}^{2} + 2x + a = 0 \: \\ equating \: it \: with \: \\ Ax^2 +Bx+C= 0 \: we \: find : \\ A = a \\ B = 2 \\ C = a \\ \because \: given \: equation \: has \: two \: distinct \: \\ real \: roots \\ \therefore \: {B}^{2} - 4AC > 0 \\ \implies \: {2}^{2} - 4 \times a \times a > 0 \\ \implies 4 - 4 {a}^{2} > 0\\ \implies 4 > 4 {a}^{2} \\ \implies \frac{4}{4} > {a}^{2} \\ \implies 1 > {a}^{2} \\ \implies \pm1 > {a} \\which \: \implies \: a < - 1 \\ thus \: \huge \fbox{ a < \: - 1}$