Question

if the equation x^2+4x+k=0has real and unequal roots then what is the value of k?​

Answer 1

Answer:

k = 4

Step-by-step explanation:

Given that f(x) = x² + 4x + k= 0 had real and equal roots.

Thus, D = b² - 4ac = 0

a = 1

b = 4

c = k

D = 4² - 4(1)(k) = 0

or 16 - 4k = 0

or - 4k = -16

or k = 4

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Answer 2

$\huge \boxed{answer}$

The given quadratic equation is x² + 4x + k = 0

A quadratic equation ax² + bx + c = 0 has real roots if

$b {}^{2} - 4ac \geqslant 0$

we have

$a = 1 \: \: \: \: b = 4 \: \: \: c = k$

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

$16 - 4k \geqslant 0$

$16 \geqslant 4k$

Divide both sides 4

$4 \geqslant k$

Therefore , the value of k must be less than or equal to 4.