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Find the roots of the equation (x-5)(x-7)=8
- a)3 ,6
- b)5,7
- c)6,9
- d)3,9
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Find the roots of the equation (x-5)(x-7)=8a)3 ,6b)5,7c)6,9d)3,9Correc...
(x-5)(x-7)=8
∴x2-12x+35=8
∴x2-12x+27=0
∴x2-9x-3x+27=0
∴x(x-9)-3(x-9)=0
∴(x-9)(x-3)=0
∴x=9 or x=3
Hence, the roots of the equation are 3 and 9
∴x2-12x+35=8
∴x2-12x+27=0
∴x2-9x-3x+27=0
∴x(x-9)-3(x-9)=0
∴(x-9)(x-3)=0
∴x=9 or x=3
Hence, the roots of the equation are 3 and 9
Most Upvoted Answer
Find the roots of the equation (x-5)(x-7)=8a)3 ,6b)5,7c)6,9d)3,9Correc...
To find the roots of the equation (x-5)(x-7) = 8, we need to solve for x.
Step 1: Expand the equation
(x-5)(x-7) = 8
x^2 - 7x - 5x + 35 = 8
x^2 - 12x + 27 = 0
Step 2: Factor the equation
To factor the quadratic equation x^2 - 12x + 27 = 0, we need to find two numbers that multiply to give 27 and add up to -12. These numbers are -3 and -9.
(x - 3)(x - 9) = 0
Step 3: Set each factor equal to zero
x - 3 = 0 or x - 9 = 0
Step 4: Solve for x
For x - 3 = 0:
x = 3
For x - 9 = 0:
x = 9
Therefore, the roots of the equation (x-5)(x-7) = 8 are x = 3 and x = 9.
Since option D states that the roots are 3 and 9, option D is the correct answer.
Summary:
The roots of the equation (x-5)(x-7) = 8 are x = 3 and x = 9.
Step 1: Expand the equation
(x-5)(x-7) = 8
x^2 - 7x - 5x + 35 = 8
x^2 - 12x + 27 = 0
Step 2: Factor the equation
To factor the quadratic equation x^2 - 12x + 27 = 0, we need to find two numbers that multiply to give 27 and add up to -12. These numbers are -3 and -9.
(x - 3)(x - 9) = 0
Step 3: Set each factor equal to zero
x - 3 = 0 or x - 9 = 0
Step 4: Solve for x
For x - 3 = 0:
x = 3
For x - 9 = 0:
x = 9
Therefore, the roots of the equation (x-5)(x-7) = 8 are x = 3 and x = 9.
Since option D states that the roots are 3 and 9, option D is the correct answer.
Summary:
The roots of the equation (x-5)(x-7) = 8 are x = 3 and x = 9.
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Find the roots of the equation (x-5)(x-7)=8a)3 ,6b)5,7c)6,9d)3,9Correc...
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Find the roots of the equation (x-5)(x-7)=8a)3 ,6b)5,7c)6,9d)3,9Correct answer is option 'D'. Can you explain this answer?
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