Question

1. The value of k for which equation 9x2 + 8xk+8 = 0 has equal roots is:
(a) only 3
(b) only -3 (c) +or-3 (d) 9​

Answer 1

Answer:

Option C

+ or - 3

Step-by-step explanation:

A quadratic equation will have equal roots if its Discriminant is equal to zero.

the discriminant in this case is $b^{2}- 4 ac$

considering the equation,

$9x^{2} + 8xk+8 = 0$

a = 9, b= 8k, c=8

Replacing the variables in the original equation with their respective values, we will have:

$8k^{2}- 4 \times 9 \times 8=0\\64k^{2}=288\\k=\sqrt{288/64} =\sqrt{9/2}$

Note: The values of k are meant to be + or -2.12 as seen from the workings

However, these are not in the options given. the closest choice to it

is + or - 3

Answer 2

The value of k must be -2.12 or 2.12.

The quadratic equation is given as:

$9x^2 + 8xk + 8 = 0$

A quadratic equation is represented as:

$ax^2 + bx + c = 0$

When it has equal roots, then

$b^2 = 4ac$

In $9x^2 + 8xk + 8 = 0$, we have:

$a = 9$

$b = 8k$

$c = 8$

So, the equation $b^2 = 4ac$ becomes

$(8k)^2 = 4 \times 9 \times 8$

$(8k)^2 = 288$

Evaluate the roots

$64k^2 = 288$

Divide both sides by 64

$k^2 = 4.5$

Take square roots of both sides

$k = \pm2.12$

Hence, the value of k must be -2.12 or 2.12.

So, we can conclude that none of the options is correct.

Read more about quadratic functions at:

https://brainly.com/question/11631534