Question

if one zero of the polynomial (k+1)x square -5x+5 is the multiplicative inverse of the other ,then find the zeroes of kx square -3kx+9 where k is a constant

Answer 1

if zeros of the polynomial (k+1)x^2-5x+5is the multi plicative inverse of the other then product of zeros is 1 hence 5/(k+1)=1 then k=4 now,kx^2-3kx+9 becomes 4x^2-12x+9 which is the square of (2x-3)^2 hence the zero is 2/3

Answer 2

Answer:

Zeroes are $x=\frac{3}{2}, \frac{3}{2}$

Step-by-step explanation:

Given one zero of the polynomial $(k+1)x^2-5x+5$ is the multiplicative inverse of the other, then we have to find the zeroes of the polynomial $kx^2-3kx+9$ where k is a constant

If one zero of polynomial $(k+1)x^2-5x+5$ is the multiplicative inverse of other then product of zeroes will be 1

∴ Product of zeroes= $\frac{c}{a}=\frac{5}{k+1}=1$

⇒k+1=5 ⇒ k=4

Now, the second polynomial is $kx^2-3kx+9=4x^2-12x+9$

we have to find the zeroes of above polynomial

$4x^2-12x+9=0$

⇒ $4x^2-6x-6x+9=0$

⇒ $2x(2x-3)-3(2x-3)=0$

⇒ $(2x-3)(2x-3)=0$

⇒ $x=\frac{3}{2}, \frac{3}{2}$

Hence, zeroes are $x=\frac{3}{2}, \frac{3}{2}$