If k is a negative number and 2k28 - k2 - 1- calculate the value of k-

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Introduction

If k is a n...

Question

If $k$ is a negative number and $\frac{(2 k)^{2}}{8} + \frac{k}{2} = 1$ , calculate the value of $k$ .

- 4

No worries! We‘ve got your back. Try BYJU‘S free classes today!

- 3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

- 2

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

- 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $- 2$
Work with the answers, plugging them in for $k$ until the equation works.
You will see that when $k = 2$ , the left-hand side of the equation becomes:
$\frac{(- 4)^{2}}{8} + \frac{- 2}{2} = \frac{16}{8} - \frac{2}{2} = 2 - 1 = 1$
So that answer C is correct.
Or use algebra to solve the equation:
$\frac{(2 k)^{2}}{8} + \frac{k}{2} = \frac{k^{2}}{2} + \frac{k}{2} = 1$ .
Multiply both sides by $2$ and put everything on one side:
$k^{2} + k - 2 = 0$ .
Factor this to get:
$(k + 2) (k - 1) = 0$ ,
So that $k = - 2$ , since we need the negative solution.

Suggest Corrections

Similar questions

Q. The set of values of

k

for which the equation

x^{4} + (k - 1) x^{3} + x^{2} + (k - 1) x + 1 = 0

has

2

positive and

2

negative roots is

Q. A random variable

X

has the following p.d.f.

$X$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$
$P (X = x)$	$0$	$k$	$2 k$	$2 k$	$3 k$	$k^{2}$	$2 k^{2}$	$7 k^{2} + k$

The value of

k

If $k_{1}, k_{2}, k_{3}$ are real numbers and the equation $k_{1} x^{2} + k_{2} x + k_{3} = 0$ have three roots, then value of $k_{1} + k_{2} + k_{3}$ is

Q. Find the values of k for which the roots are real and equal in each of the following equations:

(i)

k x^{2} + 4 x + 1 = 0

(ii)

k x^{2} - 2 \sqrt{5} x + 4 = 0

(iii)

3 x^{2} - 5 x + 2 k = 0

(iv)

4 x^{2} + k x + 9 = 0

(v)

2 k x^{2} - 40 x + 25 = 0

(vi)

9 x^{2} - 24 x + k = 0

(vii)

4 x^{2} - 3 k x + 1 = 0

(viii)

x^{2} - 2 (5 + 2 k) x + 3 (7 + 10 k) = 0

(ix)

(3 k + 1) x^{2} + 2 (k + 1) x + k = 0

(x)

k x^{2} + k x + 1 = - 4 x^{2} - x

(xi)

(k + 1) x^{2} + 2 (k + 3) x + (k + 8) = 0

(xii)

x^{2} - 2 k x + 7 k - 12 = 0

(xiii)

(k + 1) x^{2} - 2 (3 k + 1) x + 8 k + 1 = 0

(xiv)

(2 k + 1) x^{2} + 2 (k + 3) x + (k + 5) = 0

(xvii)

4 x^{2} - 2 (k + 1) x + (k + 4) = 0

Q. If

(k - 2) x^{2} + 8 x + k + 4 = 0

has both roots real, distinct and negative, then k =

Join BYJU'S Learning Program

If k is a negative number and (2k)28+k2=1, calculate the value of k.

If $k$ is a negative number and $\frac{(2 k)^{2}}{8} + \frac{k}{2} = 1$ , calculate the value of $k$ .