Question

The 2nd degree equation 4x² +20x+k=0,has only one solution. find the value of k.
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Answer 1

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Given :

P(x) = 4x² + 20x + k = 0

has only one solution..

To Find :

The value of 'k'..

Solution -

Here, it's given that the equation has one root

it means that the discriminant (D) must be equal to zero(0)

4x² + 20x + k = 0

in this equation ,

a = 4

b = 20

c = k

using formula for discriminant

$D = {b}^{2} - 4ac$

D = (20)² - 4(4)(k)

0 = 400 - 16k [D=0]

16k = 400

k = 25

so, the value of K is 25.

Answer 2

Answer:

P(x) = 4x² + 20x + k = 0

has only one solution..

To Find :

The value of 'k'..

Solution -

Here, it's given that the equation has one root

it means that the discriminant (D) must be equal to zero(0)

4x² + 20x + k = 0

this equation ,

a = 4

b = 20

c = k

using formula for discriminant

D = {b}^{2} - 4acD=b

2

−4ac

D = (20)² - 4(4)(k)

0 = 400 - 16k [D=0]

16k = 400

k = 25

so, the value of K is 25.