Solve the quadratic equation (x - 1)² -5(x-1)+6=0
Answers
Given equation:-
- (x - 1)² - 5(x - 1) + 6 = 0
To:-
- Solve and find the zeroes of the equation.
Solution:-
(x - 1)² - 5(x - 1) + 6 = 0
By using the identity:-
(a - b)² = a² + b² - 2ab
= {(x)² + (1)² - 2 × x × 1} - 5x + 5 + 6 = 0
= x² + 1 - 2x - 5x + 5 + 6 = 0
Taking like terms together,
x² - 2x - 5x + 1 + 5 + 6 = 0
=> x² - 7x + 12 = 0
By splitting the middle term,
= x² - 4x - 3x + 12 = 0
=> x(x - 4) - 3(x - 4) = 0
=> (x - 4) (x - 3) = 0
Either,
x - 4 = 0
=> x = 4
Or,
x - 3 = 0
=> x = 3
Therefore, the two zeroes of the given quadratic equation are 4 and 3.
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Verification:-
Sum of zeroes = -(Coefficient of x)/Coefficient of x²
= 4 + 3 = -(-7)/1
=> 7 = 7
Product of zeroes = Constant Term/Coefficient of x²
= 4 × 3 = 12/1
=> 12 = 12
Hence, Verified!!!
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How to solve?
→ Firstly we removed the first bracket by applying the identity and then the second bracket. Then we brought the like terms together. After adding the like terms we got a quadratic equation which is in the form ax² + bx + c. So by splitting the middle term we got the two zeroes of the quadratic equation.
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Explanation:
Given equation:-
(x - 1)² - 5(x - 1) + 6 = 0
To:-
Solve and find the zeroes of the equation.
Solution:-
(x - 1)² - 5(x - 1) + 6 = 0
By using the identity:-
(a - b)² = a² + b² - 2ab
= {(x)² + (1)² - 2 × x × 1} - 5x + 5 + 6 = 0
= x² + 1 - 2x - 5x + 5 + 6 = 0
Taking like terms together,
x² - 2x - 5x + 1 + 5 + 6 = 0
=> x² - 7x + 12 = 0
By splitting the middle term,
= x² - 4x - 3x + 12 = 0
=> x(x - 4) - 3(x - 4) = 0
=> (x - 4) (x - 3) = 0
Either,
x - 4 = 0
=> x = 4
Or,
x - 3 = 0
=> x = 3
Therefore, the two zeroes of the given quadratic equation are 4 and 3.
________________________________
Verification:-
Sum of zeroes = -(Coefficient of x)/Coefficient of x²
= 4 + 3 = -(-7)/1
=> 7 = 7
Product of zeroes = Constant Term/Coefficient of x²
= 4 × 3 = 12/1
=> 12 = 12
Hence, Verified!!!
________________________________
How to solve?
→ Firstly we removed the first bracket by applying the identity and then the second bracket. Then we brought the like terms together. After adding the like terms we got a quadratic equation which is in the form ax² + bx + c. So by splitting the middle term we got the two zeroes of the quadratic equation.
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