Question

the equation x2 + 2x + 1= (4-kx) 2 +3 will be quadratic , if the value of k is:​

Answer 1

Answer:

Step-by-step explanation:

$x^2 +2x +1 = (4-kx)^2+3\\or, x^2+2x+1 = 16 +k^2x^2-8kx +3\\or,(1-k^2)x^2+(2+8k)x -18=0$

Now we know that quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax2 + bx + c where a, b, c, ∈ R and a ≠ 0

if a=0, then the equation is linear, not quadratic, as there is no ax^2 term.

So, the above equation is quadratic only when

$1 - k^2 \neq 0\\or, k \neq \pm1$

Therefore, the given equation will be quadratic if  $k \in \mathbb{R} - \{-1,1\}$

Answer 2

Quadratic Equation

Given:

A quadratic equation $x^{2} +2x+1=(4-kx)^{2}+3$

To find:

The value of k for this equation to be quadratic.

Explanation:

Quadratic equations are the polynomial equations of degree 2 in one variable of type $f(x) = ax^2 + bx + c$ where $a, b, c$ ∈$R$  and $a$ ≠ $0$ .

$=>x^{2} +2x+1=16+k^{2} x^{2} -8kx+3\\=>x^{2} (1-k ^{2})+2x(1+4k)-18=0$

So, $1-k^{2}$ ≠ $0$

∴ $k$ ≠ ± $1$

Hence, given equation will be quadratic if k will be all values except 1,

or we can say that k belongs to the range of all real numbers excluding 1,

It can be denoted as $k$ ∈ $R-${1,-1}.