Question

the quadratic equation 2 x2 + k x + 3=0 has two equal roots . then find the value of k​

Answer 1

Answer:

k = 2√6

Given:

Quadratic Equation:

$2 {x}^{2} + kx + 3 = 0$

Explanation:

The roots of a quadratic equation are equal when discriminant is equal to zero.

${b}^{2} - 4ac \: is \: equal \: to \: zero$

Here,

a = 2

b = k

c = 3

Substituting the value of a, b and c in the discriminant.

$\tt {b}^{2} - 4ac = 0 \\\tt {k}^{2} - 4 \times 2 \times 3 = 0 \\ \tt {k}^{2} - 24 = 0 \\ \tt {k}^{2} = 24 \\ \tt \: k = 2 \sqrt{6}$

Therefore,

k = 2√6

Other Conditions:

$\tt \: 1) \: two \: real \: and \: distinct \: roots \: = {b}^{2} - 4ac > 0 \\\tt 2) \: two \: real \: roots \: if \: and \: only \: if = {b}^{2} - 4ac \geqslant 0 \\\tt3) \: no \: real \: roots \: if \: and \: only \: if \: = {b}^{2} - 4ac \leqslant 0$

$\tt \: if \: \sqrt{ {b}^{2} - 4ac} \: is \: negative\: then \: the\: root \: is \\ \tt \: complex \: and \: imaginary$