Question

If alpha and beta are the zeroes of the polynomial 6y 2 -7y +2 Find the quadratic polynomial whose zeroes are 1/alpha and 1/beta

Answer 1

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Answer 2

Answer:

$\frac{1}{\alpha}+\frac{1}{\beta}=\frac{7}{2}$

Step-by-step explanation:

The given quadratic polynomial is

$6y^2-7y+2$

Let us factor this polynomial using the middle term splitting method.

The middle term is -7 which can be written as -7y = -4y-3y

$6y^2-4y-3y+2\\\\2y(3y-2)-1(3y-2)\\\\(3y-2)(2y-1)$

Hence, the zeros of the polynomial are

$3y-2 =0\\\\y=\frac{2}{3}$

$2y-1 =0\\\\y=\frac{1}{2}$

Hence,

$\alpha=\frac{2}{3},\beta=\frac{1}{2}$

Thus,

$\frac{1}{\alpha}+\frac{1}{\beta}=1/\frac{2}{3}+1/\frac{1}{2}\\\\\frac{3}{2}+2\\\\=\frac{7}{2}$