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Find the zeroes of each of the following quadratic polynomials and verify the relationship
between the zeroes and their co efficient: p(x)=x square+ 2 root 2x +6?
between the zeroes and their co efficient: p(x)=x square+ 2 root 2x +6?
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Find the zeroes of each of the following quadratic polynomials and ver...
Zeroes of Quadratic Polynomial p(x)=x^2+2√2x+6
To find the zeroes of the quadratic polynomial p(x), we need to solve the equation p(x) = 0.
Using the Quadratic Formula:
Substituting the given values into the formula, we get:
Relationship between Zeroes and Coefficients:
Comparing Coefficients:
Conclusion:
To find the zeroes of the quadratic polynomial p(x), we need to solve the equation p(x) = 0.
Therefore, we have:
x^2 + 2√2x + 6 = 0
Using the Quadratic Formula:
x = [-b ± √(b^2 - 4ac)]/2a
Substituting the given values into the formula, we get:
x = [-2√2 ± √(4 + 24)]/2
x = [-2√2 ± √28]/2
x = -√2 ± √7
Relationship between Zeroes and Coefficients:
Let the zeroes of the quadratic polynomial p(x) be a and b. Then, we have:
p(x) = (x-a)(x-b)
p(x) = x^2 - (a+b)x + ab
Comparing Coefficients:
We can see that:
a+b = -2√2/1 = -2√2
ab = 6/1 = 6
Substituting the values of a and b, we get:
a*b = (-√2 + √7)(-√2 - √7)
a*b = 2 + 7 = 9
Therefore, we have:
a+b = -2√2
ab = 9
Conclusion:
Thus, we can see that the zeroes of the quadratic polynomial p(x) are -√2 + √7 and -√2 - √7. We can also verify that the relationship between the zeroes and their coefficients holds true, as shown above.
Community Answer
Find the zeroes of each of the following quadratic polynomials and ver...
I think that the quadratic equation should be x²+2√2x -6 .
Please check and tell.
Please check and tell.
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Find the zeroes of each of the following quadratic polynomials and verify the relationshipbetween the zeroes and their co efficient: p(x)=x square+ 2 root 2x +6?
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Find the zeroes of each of the following quadratic polynomials and verify the relationshipbetween the zeroes and their co efficient: p(x)=x square+ 2 root 2x +6? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Find the zeroes of each of the following quadratic polynomials and verify the relationshipbetween the zeroes and their co efficient: p(x)=x square+ 2 root 2x +6? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the zeroes of each of the following quadratic polynomials and verify the relationshipbetween the zeroes and their co efficient: p(x)=x square+ 2 root 2x +6?.
Find the zeroes of each of the following quadratic polynomials and verify the relationshipbetween the zeroes and their co efficient: p(x)=x square+ 2 root 2x +6? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Find the zeroes of each of the following quadratic polynomials and verify the relationshipbetween the zeroes and their co efficient: p(x)=x square+ 2 root 2x +6? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the zeroes of each of the following quadratic polynomials and verify the relationshipbetween the zeroes and their co efficient: p(x)=x square+ 2 root 2x +6?.
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