Question

If alpha and beta are the zeros of the polynomial 25^ x 2 – 15x + 2 then form the polynomial whose zeros are 2Alpha and 2Beta


Plz try not to give wrong answers.

Answer 1

Answer:

• x² - 6x/5 + 8/25

Explanation:

Given polynomial,

⇒ 25x² - 15x + 2

On comapring with the general form of equation ax² + bx + c

• a = 25
• b = -15
• c = 2

Then,

• Sum of zeros = α + β = -b/a = 15/25 = 3/5 . . . . . . (i)
• Product of zeroes = αβ = c/a = 2/25. . . . (ii)

Now, given zeros are 2α & 2β

So, sum of the new zeros,

= 2α + 2β

= 2(α + β)

From (i) :-

= 2(3/5)

= 6/5

And also, product of new zeros,

= 2α.2β

= 4αβ

From (ii) :-

= 4(2/25)

= 8/25

Forming a quadratic equation,

⇒ x² - (sum of zeros)x + product of zeros

⇒ x² - (6/5)x + 8/25

⇒ x² - 6x/5 + 8/25

Required answer: x² - 6x/5 + 8/25