Question

Find the value of k for quadratic equations kxof x-2+6 equal to 0

Answer 1

${\purple{\underline{\underline{\large{\mathtt{Answer:}}}}}}$

Given:

• We have been given an equation kx(x - 2) + 6 = 0.

To Find:

• We need to find the value of k.

Solution:

The given equation is kx(x - 2) + 6 = 0.

= kx^2 - 2kx + 6 = 0_____(1)

Here, a = k, b = -2k and c = 6.

We know that for equal roots, b^2 - 4ac = 0.

Substituting the values from equation 1 we have,

(-2k)^2 - 4(k)(6) = 0

=> 4k^2 - 24k = 0

=> 4k(k - 6) = 0

Either 4k = 0 or (k - 6) = 0

when 4k = 0

=> k = 0/4

=> k = 0

When (k - 6) = 0

=> k = 6

But k cannot be zero as it does not satisfy the equation, therefore the value of k is 6.

Hence, the value of k is 6.

Answer 2

Answer:

$\implies$ The value of k is 6.

$\large\underline\mathrm{Given:-}$

• We have been given an equation kx(x - 2) + 6 = 0

$\large\underline\mathrm{To \: find}$

• We need to find the value of k.

$\large\underline\mathrm{Solution}$

the given equation is kx(x - 2) + 6 = 0.

$\implies$ kx² - 2x + 6 = o. ...(1)

Now,

$\implies$ a = k

$\implies$ b = -2k

$\implies$ c = 6

Using formula:

We know that for equal roots, b² - 4ac = 0

$\implies$ (-2k)² - 4(k)(6) = 0

$\implies$ 4k² - 24k = 0

$\implies$ 4k(k - 6) = 0

$\implies$ 4k = 0 or k - 6 = 0

$\implies$ k = 0/4 or k = 6

but the k can't be zero as it doesn't satisfied the equation therefore the value of k = 6.

Hence ,

The value of k is 6.