Question

for what value of k the roots of the equation X2+4x+k=0 has equal roots
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Answer 1

EXPLANATION.

To find value of k of the roots of the equation,

⇒ x² + 4x + k = 0.

As we know that,

D = Discriminant  Or  b² - 4ac.

D = 0 Roots are real and equal.

⇒ b² - 4ac = 0

⇒ (4)² - 4(1)(k) = 0.

⇒ 16 - 4k = 0.

⇒ 4k = 16.

⇒ k = 4.

                                                                                                                     

MORE INFORMATION.

Nature of the factors of the quadratic expression.

(1) = Real ad different, if b² - 4ac > 0.

(2) = Rational and different, if b² - 4ac is a perfect square.

(3) = Real and equal, if b² - 4ac = 0.

(4) = If D < 0 Roots are imaginary and unequal or complex conjugate.

Answer 2

Answer:

k = 4

Step-by-step explanation:

Question:

For what value of k the roots of the equation $\bf{x^2+4x+k=0}$ has equal roots?

Given:

• A quadratic equation: ${x^2+4x+k=0}$
• Has equal roots

To find:

• The value of k

Solution:

As $\bf{x^2+4x+k=0}$ has equal roots, their discriminant = 0

That is, D = $\mathtt{b^2-4ac=0}$

$\mathtt{b^2-4ac=0}$

Here,

• b = 4
• a = 1
• c = k

So,

$\mathtt{4^2-4(1)(k) =0}$

16-4k = 0

-4k=-16

k = 4

Final answer:

k = 4