Question

If alpha and beta are the two zeroes of the quadratic polynomial x^2 +2x -35, find a quadratic polynomial whose zeroes are 1/alpha and 1/beta.​

Answer 1

Answer:

X^2-4x-60

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Step-by-step explanation:

Answer 2

Solution :-

Given that, ɑ and β are the he two zeroes of the quadratic polynomial x^2 +2x -35 .

So,

→ sum of roots = (-b/a)

→ ɑ + β = (-2)/1 = (-2)

and,

→ Product of roots = c/a

→ ɑ * β = (-35/1) = (-35)

______________

Now,

we have to find a quadratic polynomial whose zeroes are 1/ɑ and 1/β.

So,

→ sum of roots = 1/ɑ + 1/β

→ 1/ɑ + 1/β = (ɑ² + β²)/(ɑ * β)

→ 1/ɑ + 1/β = {(ɑ + β)² - 2ɑβ}/(ɑ * β)

Putting values now , we get,

→ 1/ɑ + 1/β = {(-2)² - 2(-35)} /(-35)

→ 1/ɑ + 1/β = {4 + 70} /(-35)

→ 1/ɑ + 1/β = (-74)/35

and,

→ Product of roots = 1/ɑ * 1/β

→ 1/ɑ * 1/β = 1/(ɑβ)

→ 1/ɑ * 1/β = (-1)/35

______________

Therefore,

→ Required Equation = x² - (sum of roots)x + Product of roots = 0

→ x² - (-74/35)x + (-1/35) = 0

→ (35x² + 74x - 1)/35 = 0

→ 35x² + 74x - 1 = 0 (Ans.)