Math, asked by shreygupta888pbh6z2, 1 year ago

Form quadratic equation when one root = 3-√5, sum of roots = 6.

Answers

Answered by Panzer786
12
Heya !!!


Let other zero be Beta .

Alpha = ( 3 - ✓5 )

Sum of zeroes = 6



Alpha + Beta = 6


3 - ✓5 + Beta = 6


Beta = ( 6 - 3 + ✓5 ) = ( 3 + ✓5 )



★ Product of zeroes = Alpha × Beta = ( 3 - ✓5 ) ( 3 + ✓5 ) = (3)² - (✓5)² = 9-5 = 4



Therefore,


Required quadratic polynomial = X²-(Sum of zeroes)X + Product of zeroes



=> X² - ( 6 )X +4


=> X² - 6X + 4 .


★ HOPE IT WILL HELP YOU ★
Answered by VijayaLaxmiMehra1
10
Hey!!

 \alpha  = 3 -  \sqrt{5}  \\  \\

Sum of zeroes = 6
 \alpha  +  \beta  = 6 \\  \\  =  > 3 -  \sqrt{5}  +  \beta  = 6 \\  \\  =  >  \beta  = 6 - 3 +  \sqrt{5}  \\  \\  =  >  \beta  = 3 +  \sqrt{5}  \\  \\
Product of zeroes
 \alpha  \times  \beta   \\  \\  =  > (3 -   \sqrt{5} ) \times (3 +  \sqrt{5} ) \\  \\  =  > (3) {}^{2}  -  \sqrt{5}  {}^{2}  \\  \\  =  > 9 - 5 \\  \\  =  > 4 \\  \\
Required polynomial
 =   > x {}^{2}  - ( \alpha  +  \beta ) x+ ( \alpha  \beta ) \\  \\  =  > x {}^{2}  - 6x + 4 >  > answer \\  \\

HOPE IT WILL HELPS YOU :-)
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