Question

if the zero of polynomial f(x)=k^2x^2-17x+k+2 are reciprocal of each other then the value of k

Answer 1

the value of K is given in solution

Answer 2

Answer:

The value of k are -1 and 2.

Step-by-step explanation:

The given polynomial is

$f(x)=k^2x^2-17x+k+2$

If the roots of a quadratic equation are α and β.

$ax^2+bx+c=0$

then

$\alpha +\beta=\frac{-b}{a}$

$\alpha \times\beta=\frac{c}{a}$

It is given that the zeroes are reciprocal of each other. Let the zeroes are α and 1/α.

$\alpha \times\frac{1}{\alpha}=\frac{k+2}{k^2}$

$1=\frac{k+2}{k^2}$

$k^2=k+2$

$k^2-k-2=0$

$k^2-2k+k-2=0$

$k(k-2)+1(k-2)=0$

$(k-2)(k+1)=0$

$x=2,-1$

Therefore the value of k are -1 and 2.