Question

if alpha and beta are the zeroes of the polynomial x^2-2x+3,then form a quadratic polynomial whose zeroes are alpha+2and beta+2​

Answer 1

Answer:

see attachment

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in sch questuon you have to find only sum and priduct of new roots

Answer 2

Answer:

x² - 6x + 11

Step by Step explanation:

The polynomial given is x²-2x+3

a = 1,

b = (-2),

c = 3

α and β are the roots.

We can say that

α+β = (-b/a) = 2

αβ = (c/a) = 3

Now, let (α+2) and (β+2) be the roots of the required polynomial

Sum of the roots

= α+2+β+2

= (α+β)+4

But α+β = 2

Therefore, sum of roots of new polynomial = 2+4 = 6

Product of roots

= (α+2)(β+2)

= 4 + 2(α+β) + αβ

Substituting values of (α+β) and αβ, we get

Product of roots = 4+(2×2)+3 = 11

But we know sum of roots of polynomial is (-b/a) and product of roots is (c/a)

So

(-b/a) = 6

c/a = 11

Comparing, we get

a = 1

b = (-6)

c = 11

So the required polynomial is

ax² + bx + c

= x²-6x+11

HOPE THIS HELPS!!