Question

If one zero of the polynomial (k+1)x^2 - 5x +5 is multiplicative inverse of the other then find the zeroes of kx^2 -3kx +9

Answer 1

Answer:

The required zeros are $\frac{3}{2},\frac{3}{2}$

Step-by-step explanation:

Let the zeros of the polynomial

$(k+1)x^2-5x+5$ be$a\:and\frac{1}{a}$

Product of the zeros$=\frac{5}{k+1}$

That is,

$a.\frac{1}{a}=\frac{5}{k+1}$

$1=\frac{5}{k+1}$

$k+1=5$

$k=4$

Now, the equation $kx^2-3kx+9$ becomes

$4x^2-12x+9$

$=(2x)^2-2(2x)(3)+3^2$

$=(2x-3)^2$

$=(2x-3)(2x-3)$

$=4(x-\frac{3}{2})(x-\frac{3}{2})$

The required zeros are $\frac{3}{2},\frac{3}{2}$

Answer 2

the required zeroes are 3/2 , 3/2