Question

If alpha and beta are the roots of the equation 9x^2+7x+6=0 then the equation whose roots

are 3alpha+2 and 3beta +2​

Answer 1

Compare given equation 9x² + 7x + 6 = 0 , with ax² + bx + c = 0 .

⇒ a = 9 , b = 7 , c = 6

Given α , β are roots of the equation .

Now , Sum of roots ,

⇒ α + β = -b/a = - 7 / 9 ... (1)

Product of roots ,

⇒ αβ = c/a = 6 / 9 = 2 / 3 ... (2)

Now our required ,

$\rightarrow \bf{(3\alpha +2)(3\beta+2 )}\\\\\rightarrow \bf{9\alpha\beta +6\alpha+6\beta +4 }\\\\\rightarrow \bf{9(\alpha.\beta )+6(\alpha+\beta )+4\;\;[From\ (1)\;\& \;(2)]}\\\\\rightarrow \bf{9(\dfrac{2}{3})+6(\dfrac{-7}{9})+4}\\\\\rightarrow \bf{6-\dfrac{14}{3}+4}\\\\\rightarrow \bf{10-\dfrac{14}{3}}\\\\\rightarrow \bf{\dfrac{16}{3}}$

Answer 2

Answer:

16/3

Step-by-step explanation:

Compare given equation 9x² + 7x + 6 = 0 , with ax² + bx + c = 0 .

⇒ a = 9 , b = 7 , c = 6

Given α , β are roots of the equation .

Now , Sum of roots ,

⇒ α + β = -b/a = - 7 / 9 ... (1)

Product of roots ,

⇒ αβ = c/a = 6 / 9 = 2 / 3 ... (2)

Now our required ,