Question

3. if the roots of the quadratic equation x^2+6x+k=0 are equal, then the value of k is​

Answer 1

Question :

If the roots of the quadratic equation x^2+6x+k=0 are equal, then the value of k is?

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➦ x² + 6x + k = 0

❒ The quadratic equations have a real roots if b² - 4ac = 0

➦ Here a = 1, b = 6 and c = k

✔ (6)² - 4 (1) (k) = 0

✔ 36 - 4k = 0

✔ -4k = -36

✔ k = 9

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• So the value of k is 9.

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More to know:

➪ Two distinct real roots , if b² - 4ac > 0

➪ Two equal real roots , if b² - 4ac = 0

➪ No real roots if b² - 4ac < 0.

• b² - 4ac is called discriminant of a quadratic equation.

Answer 2

Answer:

$\red \bigstar$ The value of if the roots of the quadratic equation x² + 6x + k = 0 are equal is 9.

SOLUTION

The given quadratic equation is x² + 6x + k = 0

We know that , a quadratic equation will have equal roots only if the discriminant is 0.

i.e , b² - 4ac = 0.

The general form of a quadratic equation is ax² + bx + c = 0

Here,

a = 1

b = 6

c = k

Now, let us take the discriminant by substituting the values of a , b and c

$\implies$ 6² - 4 × 1 × k = 0

$\implies$ 36 - 4k = 0

$\implies$ 4k = 36

$\implies \sf k = \dfrac{36}{4}$

$\implies \sf k = 9$