Question

The equation kx2-4kx+8 is not equal to 0 has real and equal roots. Find the value of K

Answer 1

Answer

The value of k is 2

Given

The quadratic equation :

• kx² - 4kx + 8 = 0
• The given equation has real and equal roots

To Find

• The value of k

Solution

Since , the equation kx² - 4kx + 8 = 0 has real and equal roots so its discriminant b² - 4ac will be 0

Here in the equation,

a = k

b = -4k

c = 8

Since , the roots of the equation are equal

∴ b² - 4ac = 0

⇒ (-4k)² - 4× (k)(8) = 0

⇒ 16k² - 32k = 0

⇒ 16k(k - 2) = 0

⇒ k(k - 2) = 0

Thus , we have

⇒ k = 0 and k = 2

Since the equation is quadratic and putting k = 0 we will get the coefficient of x² as 0 so k ≠ 0

Hence ,value of k is 2

Answer 2

Given that ,

The polynomial is kx² - 4kx + 8 and has real and equal roots

We know that ,

The discriminant of quadratic polynomial is given by

$\large \sf \fbox{D = {(b)}^{2} - 4ac }$

Thus ,

D = (-4k)² - 4k × 8

D = 16k² - 32k

D = 16k(k - 2)

Since ,

The given polynomial has real and equal roots

Thus ,

16k(k - 2) = 0

k - 2 = 0

k = 2

$\therefore \sf \underline{The \: value \: of \: k \: is \: 2 \: }$