Physics, asked by Click002, 2 months ago

if alpha and beta are zeroes of the quadratic polynomial f(x) = x2+x-2 then find a polynomial whose zeroes are 2alpha + 1 and 2beta + 1​

Answers

Answered by ItzBlinkingstar
2

Answer:

f(x) = x² + x - 2

To find zeroes equate the given polynomial to 0

x² + x - 2 = 0

Splitting the middle term

x² + 2x - x - 2 = 0

x(x + 2) - 1(x + 2) = 0

(x + 2)(x - 1) = 0

x + 2 = 0 or x - 1 = 0

x = - 2 or x = 1

Zeroes of the polynomial x² + x - 2 are - 2 , 1

So

• α = - 2

• β = 1

Finding a polyinomial whose zeroes are (2α + 1) and (2β + 1)

2α + 1

= 2(-2) + 1

= - 4 + 1

(2α + 1)= - 3

2β + 1

= 2(1) + 1

= 2 + 1

(2β + 1) = 3

The new polynomial zeroes should be - 3 and 3

Here

• α = - 3

• β = 3

Sum of zeroes = α + β = - 3 + 3 = 0

Product of zeroes = αβ = - 3(3) = - 9

Quadratic polynomial ax² + bx + c = k{x² - x(α + β) + αβ}

(Where k ≠ 0)

= k{x² - x(0) + (-9)}

= k(x² - 0 - 9)

= k(x² - 9)

When k = 1

= 1(x² - 9)

= x² - 9

Therefore the polynomial is x² - 9.

Answered by sunayksingh
2

Answer:

polynomial is x² - 9.

Explanation:

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