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If the square difference of two zeroes of the quadratic polynomial of p(x) = x^2 3x k is 3. find k?
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If the square difference of two zeroes of the quadratic polynomial of ...
Problem: Find the value of k in the quadratic polynomial of p(x) = x^2 - 3x + k if the square difference of two zeroes of p(x) is 3.
Solution:
Step 1: Recall the formula for finding the zeroes of a quadratic polynomial in the form of ax^2 + bx + c = 0. The formula is given by:
x = (-b ± sqrt(b^2 - 4ac))/2a
Step 2: Use the formula to find the zeroes of the given polynomial p(x) = x^2 - 3x + k. We have:
x = (3 ± sqrt(9 - 4k))/2
Step 3: Find the square difference of the two zeroes of p(x). We have:
(3 + sqrt(9 - 4k))/2 - (3 - sqrt(9 - 4k))/2)^2
= ((3 + sqrt(9 - 4k)) - (3 - sqrt(9 - 4k)))^2/4
= (2sqrt(9 - 4k))^2/4
= (36 - 16k)/2
= 18 - 8k
Step 4: Equate the square difference of the two zeroes to 3, as given in the problem. We have:
18 - 8k = 3
Step 5: Solve for k. We have:
18 - 3 = 8k
15 = 8k
k = 15/8
Therefore, the value of k in the quadratic polynomial p(x) = x^2 - 3x + k is 15/8 when the square difference of the two zeroes of p(x) is 3.
Solution:
Step 1: Recall the formula for finding the zeroes of a quadratic polynomial in the form of ax^2 + bx + c = 0. The formula is given by:
x = (-b ± sqrt(b^2 - 4ac))/2a
Step 2: Use the formula to find the zeroes of the given polynomial p(x) = x^2 - 3x + k. We have:
x = (3 ± sqrt(9 - 4k))/2
Step 3: Find the square difference of the two zeroes of p(x). We have:
(3 + sqrt(9 - 4k))/2 - (3 - sqrt(9 - 4k))/2)^2
= ((3 + sqrt(9 - 4k)) - (3 - sqrt(9 - 4k)))^2/4
= (2sqrt(9 - 4k))^2/4
= (36 - 16k)/2
= 18 - 8k
Step 4: Equate the square difference of the two zeroes to 3, as given in the problem. We have:
18 - 8k = 3
Step 5: Solve for k. We have:
18 - 3 = 8k
15 = 8k
k = 15/8
Therefore, the value of k in the quadratic polynomial p(x) = x^2 - 3x + k is 15/8 when the square difference of the two zeroes of p(x) is 3.
Community Answer
If the square difference of two zeroes of the quadratic polynomial of ...
Value of k=2
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If the square difference of two zeroes of the quadratic polynomial of p(x) = x^2 3x k is 3. find k?
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If the square difference of two zeroes of the quadratic polynomial of p(x) = x^2 3x k is 3. find k? 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 If the square difference of two zeroes of the quadratic polynomial of p(x) = x^2 3x k is 3. find k? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the square difference of two zeroes of the quadratic polynomial of p(x) = x^2 3x k is 3. find k?.
If the square difference of two zeroes of the quadratic polynomial of p(x) = x^2 3x k is 3. find k? 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 If the square difference of two zeroes of the quadratic polynomial of p(x) = x^2 3x k is 3. find k? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the square difference of two zeroes of the quadratic polynomial of p(x) = x^2 3x k is 3. find k?.
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