8th-MATHEMATICS53. If α,β are the roots of ax2 +bx+c 0then the equat

1.	8th-MATHEMATICS53. If α,β are the roots of ax2 +bx+c 0then the equation whose roots are2+α, 2 + β is
Answer» Given α and β are roots of ax² + bx + c = 0 We know, α + β = -b/a αβ = c/a We know any polynomial have zero m and n can be written as ( x - m) ( x - n) = x² - ( m + n)x + mn So, polynomial have zeroes 2 + α and 2 + β Will be x² - (4+α+β) x + (2 + α)(2 + β) x² - ( 4 - b/a)x + (4 + 2(α + β)+αβ) x² + ( b - 4a)x/a +(4 - 2b/a + c/a)

8th-MATHEMATICS53. If α,β are the roots of ax2 +bx+c 0then the equation whose roots are2+α, 2 + β is

Answer»

Given α and β are roots of

ax² + bx + c = 0

We know, α + β = -b/a

αβ = c/a

We know any polynomial have zero m and n can be written as

( x - m) ( x - n) = x² - ( m + n)x + mn

So, polynomial have zeroes 2 + α and 2 + β

Will be

x² - (4+α+β) x + (2 + α)(2 + β)

x² - ( 4 - b/a)x + (4 + 2(α + β)+αβ)

x² + ( b - 4a)x/a +(4 - 2b/a + c/a)