Question

If m and n are the zeroes of the polynomial 6y 2 -7y – 2, find a polynomial whose zeroes are 1/m and 1/n

Answer 1

Answer:

$y^2-\frac{7}{2}y+3$

Step-by-step explanation:

Given polynomial is,

6y² - 7y - 2

Fro the zeros of the given polynomial,

6y² - 7y - 2 = 0

6y² - 4y - 3y - 2 = 0

2y(3y - 2) - 1(3y - 2) = 0

(2y - 1)(3y - 2) = 0

(2y - 1) = 0

y = $\frac{1}{2}$

(3y - 2) = 0

y = $\frac{2}{3}$

Therefore, zeros of this polynomial are m = $\frac{1}{2}$ and n = $\frac{2}{3}$

If a polynomial has zeros as $\frac{1}{m}$ and $\frac{1}{n}$ then the zeros will be $\frac{3}{2}$ and 2.

Polynomial will be,

$(y-\frac{3}{2})(y-2)$

= $y(y-2)-\frac{3}{2}(y-2)$

= $y^2-2y-\frac{3}{2}y+3$

= $y^2-\frac{7}{2}y+3$