Question

For what values of k does the quadratic equation 4x² - 12x - k = 0 have no real roots ?​

Answer 1

Answer:

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Answer 2

$\huge\star{\green{\underline{\mathfrak{Answer :-}}}}$

We know that when b² - 4ac < 0, then we can say that a quadratic equation will have no real roots.

Now, the quadratic equation which is given to us is : 4x² - 12x - k = 0.

Here, a = 4

a = 4b = - 12

a = 4b = - 12c = - k.

Substituting these values,

➜ b² - 4ac < 0

➜ (- 12)² - 4(4)(- k) < 0

➜ 144 + 16k < 0

➜ 16k < 0 - 144

➜ k < - 144 / 16

➜ k < - 9

Now, so the values of k will be obviously less than -9.

We can say that the value of k will be between -infinity and -9.

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