Question

Find, for what values of ‘' does the quadratic
equation x² + 2x+k2-3= 0, has real and
equal roots.​

Answer 1

AnsWer :

K = 2.

Correct QuestioN :

Find the value of K does the Quadratic Equation x² + 2x + k² - 3 = 0. has real and equal roots.

SolutioN :

We have, Quadratic Equation.

x² + 2x + k² - 3 = 0.

D = b² - 4ac.

Where as,

• D Discriminate.
• a = 1.
• b = 2.
• c = k² - 3.

→ D = ( 2 )² - 4 * 1 * ( k² - 3 )

→ D = 4 - 4( k² + 3 )

→ D = 4 - 4k² + 12.

$\rule{200}2$

☛ Condition :

• Both roots are Real and Equal.
• D = 0.

$\rule{200}2$

→ 0 = 4 + 12 - 4k²

→ 0 = 16 - 4k².

→ 4k² = 16

→ k² = 4

→ k = ± 2.

✡ Therefore, the value k is ± 2.