Question

if 4 x square + 4 + kx is equal to zero has equal roots then K is equal to

Answer 1

comparing the eqn with ax^2+bx+c=0
so,a=4,b=k,c=4
b^2-4ac=k^2-4*4*4
            =k^2-64
as it has real and equal roots.
b^2-4ac = 0

k^2-64=0
k^2=64

taking square root on both sides

k=8  or k= -8

Answer 2

The value of k = ± 8

Given :

4x² + 4 + kx = 0 has equal roots

To find :

The value of k

Concept :

1. General form of a quadratic equation is

ax² + bx + c = 0

The Discriminant of the quadratic equation is denoted by D and defined as

D = b² - 4ac

2. If a quadratic equation has equal roots then discriminant of the equation = 0

Solution :

Step 1 of 3 :

Write down the given Quadratic equation

Here the given Quadratic equation is

4x² + 4 + kx = 0

Step 2 of 3 :

Find the discriminant

4x² + 4 + kx = 0

⇒4x² + kx + 4 = 0

Comparing with the general equation ax² + bx + c = 0 we get

a = 4 , b = k , c = 4

Hence discriminant of the quadratic equation

= b² - 4ac

$\sf = {( k) }^{2} - 4 \times 4 \times 4$

$\sf = {k} ^{2} - 64$

Step 3 of 3 :

Find the value of k

Since the quadratic equation has equal roots

∴ Discriminant of the equation = 0

$\displaystyle \sf{ \implies {k}^{2} } - 64 = 0$

$\displaystyle \sf{ \implies {k}^{2} } = 64$

$\displaystyle \sf{ \implies k = \pm \: \sqrt{64} }$

$\displaystyle \sf{ \implies k = \pm \: 8 }$

Hence the required value of k = ± 8

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