Question

.find the value of k so that the quadratic equation 3x2 -2kx + 12= 0 has equal roots

Answer 1

Given :

Quadratic equation ; 3x² - 2kx + 12 = 0 has equal roots.

To find :

Value of k.

Concept :

· If discriminant ; D = 0 , then quadratic equation will have real and equal roots.

· If D > 0 , quadratic equation will have real and distinct roots.

· If D < 0, quadratic equation will have imaginary roots.

Solution :

As the quadratic equation will have equal roots, so D = 0

Now comparing the given equation with ax² + bx + c = 0, we get :

· a = 3

· b = -2k

· c = 12

Now we know,

⇒ D = b² - 4ac = 0

⇒ (-2k)² - 4(3)(12) = 0

⇒ 4k² - 144 = 0

⇒ 4k² = 144

⇒ k² = 144/4

⇒ k² = 36

⇒ k = √36

⇒ k = ±6

∴ Required value of k = ±6

Answer 2

For equal roots of a quadratic equation,

Discriminant = 0

→ b² - 4ac = 0

Here,

• a = 3
• b = -2k
• c = 12

So,

Discriminant = 0

→ (-2k)² - 4(3)(12) = 0

→ 4k² - 144 = 0

→ k² = 144/4

→ k² = 36

→ k = √36

→ k = ± 6