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SVEN [57.7K]
2 years ago
10

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

Mathematics
1 answer:
denis-greek [22]2 years ago
7 0

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

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