[tex]\underline{\underline{\bf{Question : -}}}[/tex]
For some integer q, every positive odd integer is of the form :
[tex]\underline{\underline{\bf{Answer : -}}}[/tex]
Let the positive odd integer be a and b = 2
As we know that :
[tex]\:\:\:\:\:\:\:\:\:\:[/tex] [tex]\implies[/tex][tex]\color{black}\boxed{a = bq + r}[/tex]
If b = 2 Then,
[tex]\:\:\:\:\:\:\:\:\:\:[/tex] [tex]\implies\sf{a = 2q + r}[/tex][tex]\:\:\:\:\:\:\:\:\:\:[/tex] [tex]\sf{[0 < r < b]}[/tex]
Positive value of 2 where,
r = 0 , a = 2q + 0 ; 2q
r = 1 , a = 2q + 1
r = 2 , a = 2q + 2
Hence , any positive odd integer is in the form of 2q, 2q + 1 and 2q + 2
[tex]\rule{200pt}{4pt}[/tex]
Find the zeroes of the Quadratic Equation [tex]\sf{x² + 5x + 6}[/tex]
[tex]\:\:\:\:\:\:\:\:\:\:[/tex] [tex]\implies\sf{x² + 5x + 6 = 0}[/tex]
By Middle term splitting:
[tex]\:\:\:\:\:\:\:\:\:\:[/tex] [tex]\implies\sf{x² + 2x + 3x+ 6 = 0}[/tex]
[tex]\:\:\:\:\:\:\:\:\:\:[/tex] [tex]\implies\sf{x (x + 2) +3 (x + 2 ) = 0}[/tex]
[tex]\:\:\:\:\:\:\:\:\:\:[/tex] [tex]\implies\sf{ (x + 2) (x + 3 ) = 0}[/tex]
Hence (x + 2) and (x + 3) are the zeroes
Answer:
Question:-
Solution:-
x² + 5x + 6 = 0.
=> x² + 3x + 2x + 6 = 0.
=> x(x + 2) + 3(x + 2) = 0.
=> (x + 2)(x + 3) = 0.
=> x + 2 = 0 or x + 3 = 0.
Hence, the zeros of the quadratic polynomial x² + 5x + 6 are -2 and -3.
Copyright © 2024 EHUB.TIPS team's - All rights reserved.
Answers & Comments
Verified answer
[tex]\underline{\underline{\bf{Question : -}}}[/tex]
For some integer q, every positive odd integer is of the form :
[tex]\underline{\underline{\bf{Answer : -}}}[/tex]
Let the positive odd integer be a and b = 2
As we know that :
[tex]\:\:\:\:\:\:\:\:\:\:[/tex] [tex]\implies[/tex][tex]\color{black}\boxed{a = bq + r}[/tex]
If b = 2 Then,
[tex]\:\:\:\:\:\:\:\:\:\:[/tex] [tex]\implies\sf{a = 2q + r}[/tex][tex]\:\:\:\:\:\:\:\:\:\:[/tex] [tex]\sf{[0 < r < b]}[/tex]
Positive value of 2 where,
r = 0 , a = 2q + 0 ; 2q
r = 1 , a = 2q + 1
r = 2 , a = 2q + 2
Hence , any positive odd integer is in the form of 2q, 2q + 1 and 2q + 2
[tex]\rule{200pt}{4pt}[/tex]
[tex]\underline{\underline{\bf{Question : -}}}[/tex]
Find the zeroes of the Quadratic Equation [tex]\sf{x² + 5x + 6}[/tex]
[tex]\underline{\underline{\bf{Answer : -}}}[/tex]
[tex]\:\:\:\:\:\:\:\:\:\:[/tex] [tex]\implies\sf{x² + 5x + 6 = 0}[/tex]
By Middle term splitting:
[tex]\:\:\:\:\:\:\:\:\:\:[/tex] [tex]\implies\sf{x² + 2x + 3x+ 6 = 0}[/tex]
[tex]\:\:\:\:\:\:\:\:\:\:[/tex] [tex]\implies\sf{x (x + 2) +3 (x + 2 ) = 0}[/tex]
[tex]\:\:\:\:\:\:\:\:\:\:[/tex] [tex]\implies\sf{ (x + 2) (x + 3 ) = 0}[/tex]
Hence (x + 2) and (x + 3) are the zeroes
[tex]\rule{200pt}{4pt}[/tex]
Answer:
Question:-
Solution:-
x² + 5x + 6 = 0.
=> x² + 3x + 2x + 6 = 0.
=> x(x + 2) + 3(x + 2) = 0.
=> (x + 2)(x + 3) = 0.
=> x + 2 = 0 or x + 3 = 0.
Hence, the zeros of the quadratic polynomial x² + 5x + 6 are -2 and -3.