Verify the relationship between coefficient of polynomial and the roots of the polynomial p(x) = 4x^2-4x+1 pls right correct answer
Answers
Hey Mate !
Here is your solution :
Given,
Quadratic eq. = 4x² - 4x + 1
Here,
Coefficient of x² ( a ) = 4
Coefficient of x ( b ) = -4
Constant term ( c ) = 1
Now,
=> 4x² - 4x + 1 = 0
=> ( 2x )² - 2 × 2x × 1 + ( 1 )² = 0
Using identity :
=> ( a² - 2ab + b² ) = ( a - b )²
=> ( 2x - 1 )² = 0
=> ( 2x - 1 ) ( 2x - 1 ) = 0 ( continued further )
=> ( 2x - 1 ) = 0 ÷ ( 2x - 1 )
=> ( 2x - 1 ) = 0
=> x = 1/2
★
=> ( 2x - 1 ) = 0 ÷ ( 2x - 1 )
=> ( 2x - 1 ) = 0
=> 2x = 1
=> x = 1/2
Hence, zeroes are ( 1/2 ) and ( 1/2 ).
Now,
=> Sum of zeroes = -b/a
=> ( 1/2 ) + ( 1/2 ) = -( -4 ) ÷ 4
=> ( 1 + 1 )/2 = 4 ÷ 4
=> 2÷2 = 1
=> 1 = 1
And,
=> Product of zeroes = c/a
=> ( 1/2 ) × ( 1/2 ) = 1/4
=> 1/4 = 1/4
★ Verified ★
Hey Mate !
Here is your solution :
Given,
Quadratic eq. = 4x² - 4x + 1
Here,
Coefficient of x² ( a ) = 4
Coefficient of x ( b ) = -4
Constant term ( c ) = 1
Now,
=> 4x² - 4x + 1 = 0
=> ( 2x )² - 2 × 2x × 1 + ( 1 )² = 0
Using identity :
=> ( a² - 2ab + b² ) = ( a - b )²
=> ( 2x - 1 )² = 0
=> ( 2x - 1 ) ( 2x - 1 ) = 0 ( continued further )
=> ( 2x - 1 ) = 0 ÷ ( 2x - 1 )
=> ( 2x - 1 ) = 0
=> x = 1/2
★
=> ( 2x - 1 ) = 0 ÷ ( 2x - 1 )
=> ( 2x - 1 ) = 0
=> 2x = 1
=> x = 1/2
Hence, zeroes are ( 1/2 ) and ( 1/2 ).
Now,
=> Sum of zeroes = -b/a
=> ( 1/2 ) + ( 1/2 ) = -( -4 ) ÷ 4
=> ( 1 + 1 )/2 = 4 ÷ 4
=> 2÷2 = 1
=> 1 = 1
And,
=> Product of zeroes = c/a
=> ( 1/2 ) × ( 1/2 ) = 1/4
=> 1/4 = 1/4
★ Verified ★
Hey Mate !
Here is your solution :
Given,
Quadratic eq. = 4x² - 4x + 1
Here,
Coefficient of x² ( a ) = 4
Coefficient of x ( b ) = -4
Constant term ( c ) = 1
Now,
=> 4x² - 4x + 1 = 0
=> ( 2x )² - 2 × 2x × 1 + ( 1 )² = 0
Using identity :
=> ( a² - 2ab + b² ) = ( a - b )²
=> ( 2x - 1 )² = 0
=> ( 2x - 1 ) ( 2x - 1 ) = 0 ( continued further )
=> ( 2x - 1 ) = 0 ÷ ( 2x - 1 )
=> ( 2x - 1 ) = 0
=> x = 1/2
★
=> ( 2x - 1 ) = 0 ÷ ( 2x - 1 )
=> ( 2x - 1 ) = 0
=> 2x = 1
=> x = 1/2
Hence, zeroes are ( 1/2 ) and ( 1/2 ).
Now,
=> Sum of zeroes = -b/a
=> ( 1/2 ) + ( 1/2 ) = -( -4 ) ÷ 4
=> ( 1 + 1 )/2 = 4 ÷ 4
=> 2÷2 = 1
=> 1 = 1
And,
=> Product of zeroes = c/a
=> ( 1/2 ) × ( 1/2 ) = 1/4
=> 1/4 = 1/4
★ Verified ★
Hey Mate !
Here is your solution :
Given,
Quadratic eq. = 4x² - 4x + 1
Here,
Coefficient of x² ( a ) = 4
Coefficient of x ( b ) = -4
Constant term ( c ) = 1
Now,
=> 4x² - 4x + 1 = 0
=> ( 2x )² - 2 × 2x × 1 + ( 1 )² = 0
Using identity :
=> ( a² - 2ab + b² ) = ( a - b )²
=> ( 2x - 1 )² = 0
=> ( 2x - 1 ) ( 2x - 1 ) = 0 ( continued further )
=> ( 2x - 1 ) = 0 ÷ ( 2x - 1 )
=> ( 2x - 1 ) = 0
=> x = 1/2
★
=> ( 2x - 1 ) = 0 ÷ ( 2x - 1 )
=> ( 2x - 1 ) = 0
=> 2x = 1
=> x = 1/2
Hence, zeroes are ( 1/2 ) and ( 1/2 ).
Now,
=> Sum of zeroes = -b/a
=> ( 1/2 ) + ( 1/2 ) = -( -4 ) ÷ 4
=> ( 1 + 1 )/2 = 4 ÷ 4
=> 2÷2 = 1
=> 1 = 1
And,
=> Product of zeroes = c/a
=> ( 1/2 ) × ( 1/2 ) = 1/4
=> 1/4 = 1/4
★ Verified ★
Hey Mate !
Here is your solution :
Given,
Quadratic eq. = 4x² - 4x + 1
Here,
Coefficient of x² ( a ) = 4
Coefficient of x ( b ) = -4
Constant term ( c ) = 1
Now,
=> 4x² - 4x + 1 = 0
=> ( 2x )² - 2 × 2x × 1 + ( 1 )² = 0
Using identity :
=> ( a² - 2ab + b² ) = ( a - b )²
=> ( 2x - 1 )² = 0
=> ( 2x - 1 ) ( 2x - 1 ) = 0 ( continued further )
=> ( 2x - 1 ) = 0 ÷ ( 2x - 1 )
=> ( 2x - 1 ) = 0
=> x = 1/2
★
=> ( 2x - 1 ) = 0 ÷ ( 2x - 1 )
=> ( 2x - 1 ) = 0
=> 2x = 1
=> x = 1/2
Hence, zeroes are ( 1/2 ) and ( 1/2 ).
Now,
=> Sum of zeroes = -b/a
=> ( 1/2 ) + ( 1/2 ) = -( -4 ) ÷ 4
=> ( 1 + 1 )/2 = 4 ÷ 4
=> 2÷2 = 1
=> 1 = 1
And,
=> Product of zeroes = c/a
=> ( 1/2 ) × ( 1/2 ) = 1/4
=> 1/4 = 1/4
★ Verified ★
Hey Mate !
Here is your solution :
Given,
Quadratic eq. = 4x² - 4x + 1
Here,
Coefficient of x² ( a ) = 4
Coefficient of x ( b ) = -4
Constant term ( c ) = 1
Now,
=> 4x² - 4x + 1 = 0
=> ( 2x )² - 2 × 2x × 1 + ( 1 )² = 0
Using identity :
=> ( a² - 2ab + b² ) = ( a - b )²
=> ( 2x - 1 )² = 0
=> ( 2x - 1 ) ( 2x - 1 ) = 0 ( continued further )
=> ( 2x - 1 ) = 0 ÷ ( 2x - 1 )
=> ( 2x - 1 ) = 0
=> x = 1/2
★
=> ( 2x - 1 ) = 0 ÷ ( 2x - 1 )
=> ( 2x - 1 ) = 0
=> 2x = 1
=> x = 1/2
Hence, zeroes are ( 1/2 ) and ( 1/2 ).
Now,
=> Sum of zeroes = -b/a
=> ( 1/2 ) + ( 1/2 ) = -( -4 ) ÷ 4
=> ( 1 + 1 )/2 = 4 ÷ 4
=> 2÷2 = 1
=> 1 = 1
And,
=> Product of zeroes = c/a
=> ( 1/2 ) × ( 1/2 ) = 1/4
=> 1/4 = 1/4
★ Verified ★
Hey Mate !
Here is your solution :
Given,
Quadratic eq. = 4x² - 4x + 1
Here,
Coefficient of x² ( a ) = 4
Coefficient of x ( b ) = -4
Constant term ( c ) = 1
Now,
=> 4x² - 4x + 1 = 0
=> ( 2x )² - 2 × 2x × 1 + ( 1 )² = 0
Using identity :
=> ( a² - 2ab + b² ) = ( a - b )²
=> ( 2x - 1 )² = 0
=> ( 2x - 1 ) ( 2x - 1 ) = 0 ( continued further )
=> ( 2x - 1 ) = 0 ÷ ( 2x - 1 )
=> ( 2x - 1 ) = 0
=> x = 1/2
★
=> ( 2x - 1 ) = 0 ÷ ( 2x - 1 )
=> ( 2x - 1 ) = 0
=> 2x = 1
=> x = 1/2
Hence, zeroes are ( 1/2 ) and ( 1/2 ).
Now,
=> Sum of zeroes = -b/a
=> ( 1/2 ) + ( 1/2 ) = -( -4 ) ÷ 4
=> ( 1 + 1 )/2 = 4 ÷ 4
=> 2÷2 = 1
=> 1 = 1
And,
=> Product of zeroes = c/a
=> ( 1/2 ) × ( 1/2 ) = 1/4
=> 1/4 = 1/4
★ Verified ★
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