Question

If the roots of quadratic equation 3x^2-kx+3=0 has two real equal roots then the value of k is​

Answer 1

Required Answer :

$\boxed{\bf{\pmb{The ~~value~~ of~~ k~~ =~~ + 6 ~~and~~ - 6}}} \red \bigstar$

Given :

• Quadratic equation = 3x² - kx + 3 = 0
• It has two equal roots.

To find :

• The value of k = ?

Solution :

Here, we will use the discriminant formula to calculate the value of k.

• D = b² - 4ac

Comparing the equation 3x² - kx + 3 = 0 with ax² + bx + c = 0, we have :

• a = 3
• b = - k
• c = 3

⇒ b² - 4ac = 0 [Because it has equal roots.]

⇒ (-k)² - 4(3)(3) = 0

⇒ k² - 36 = 0

⇒ k² = 36

⇒ Taking square root on both the sides :

⇒ k = √36

⇒ k = √(6 × 6)

⇒ k = ± 6

Therefore, the value of k = + 6 and - 6

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Knowledge Bytes :

When b² - 4ac is equal to zero, then the roots are equal.

• b² - 4ac = 0 [Real roots]

When b² - 4ac is greater than zero, then the roots are real and unequal.

• b² - 4ac > 0 [Unequal and real roots]

When b² - 4ac is less than zero, then the roots are imaginary.

• b² - 4ac < 0 [Imaginary roots]

Answer 2

Answer:

Since the roots are real and equal, ∴ D = b

2 − 4ac = 0

⇒k

2 – 4×3×3 = 0 (∵ a = 3, b = k, c = 3)

⇒k

2 = 36

⇒k = 6 or −6