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If sum of the squares of zeros of the quadratic polynomial f(x) = x2 – 8x + k is 40, find the value of k.
- a)12
- b)-12
- c)14
- d)-14
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If sum of the squares of zeros of the quadratic polynomial f(x) = x2&n...
p (x)= x^2-8x+k
p (x)=Ax^2+Bx+C(The equation is in this form)
p (x)=Ax^2+Bx+C(The equation is in this form)
Let the zeroes be 'a' and 'b'
It is given that
=> a^2+b^2=40
=> (a+b)^2 - 2ab = 40 ----1
=> a^2+b^2=40
=> (a+b)^2 - 2ab = 40 ----1
sum of zeroes
=> a+b = -B/A = -(-8)/1 = 8
=> a+b = -B/A = -(-8)/1 = 8
Product of zeroes
=> a*b = C/A = k
=> a*b = C/A = k
Substitute these values in the equation1 we get
=> 8^2 - 2k = 40
=> 64 - 2k = 40
=> 2k = 24
=> k = 12
=> 8^2 - 2k = 40
=> 64 - 2k = 40
=> 2k = 24
=> k = 12
Therefore the value of k is 12
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If sum of the squares of zeros of the quadratic polynomial f(x) = x2&n...
Sum of the Squares of Zeros of a Quadratic Polynomial
To find the sum of the squares of zeros of the quadratic polynomial \( f(x) = x^2 - 8x + k \), we will first determine the zeros of the polynomial and then calculate the sum of their squares.
Finding the Zeros of the Polynomial
The zeros of a quadratic polynomial are the values of x for which the polynomial equals zero. In this case, the polynomial is \( f(x) = x^2 - 8x + k \).
Let's assume the zeros of the polynomial are \( \alpha \) and \( \beta \). Then, we have:
\( f(\alpha) = 0 \) and \( f(\beta) = 0 \)
Substitute these values into the polynomial:
\( \alpha^2 - 8\alpha + k = 0 \)
\( \beta^2 - 8\beta + k = 0 \)
Calculating the Sum of Squares of Zeros
The sum of the squares of zeros of a quadratic polynomial is given by:
\( \alpha^2 + \beta^2 \)
From the given information, we know that the sum of the squares of zeros is 40:
\( \alpha^2 + \beta^2 = 40 \)
Substitute the zeros from the above equations:
\( \alpha^2 + \beta^2 = (8\alpha - k) + (8\beta - k) = 40 \)
\( 8(\alpha + \beta) - 2k = 40 \)
Since the sum of zeros is given by:
\( \alpha + \beta = \frac{-(-8)}{1} = 8 \)
Substitute the sum of zeros into the equation:
\( 8(8) - 2k = 40 \)
\( 64 - 2k = 40 \)
\( -2k = -24 \)
\( k = 12 \)
Therefore, the value of \( k \) is 12. Hence, the correct answer is option A.
To find the sum of the squares of zeros of the quadratic polynomial \( f(x) = x^2 - 8x + k \), we will first determine the zeros of the polynomial and then calculate the sum of their squares.
Finding the Zeros of the Polynomial
The zeros of a quadratic polynomial are the values of x for which the polynomial equals zero. In this case, the polynomial is \( f(x) = x^2 - 8x + k \).
Let's assume the zeros of the polynomial are \( \alpha \) and \( \beta \). Then, we have:
\( f(\alpha) = 0 \) and \( f(\beta) = 0 \)
Substitute these values into the polynomial:
\( \alpha^2 - 8\alpha + k = 0 \)
\( \beta^2 - 8\beta + k = 0 \)
Calculating the Sum of Squares of Zeros
The sum of the squares of zeros of a quadratic polynomial is given by:
\( \alpha^2 + \beta^2 \)
From the given information, we know that the sum of the squares of zeros is 40:
\( \alpha^2 + \beta^2 = 40 \)
Substitute the zeros from the above equations:
\( \alpha^2 + \beta^2 = (8\alpha - k) + (8\beta - k) = 40 \)
\( 8(\alpha + \beta) - 2k = 40 \)
Since the sum of zeros is given by:
\( \alpha + \beta = \frac{-(-8)}{1} = 8 \)
Substitute the sum of zeros into the equation:
\( 8(8) - 2k = 40 \)
\( 64 - 2k = 40 \)
\( -2k = -24 \)
\( k = 12 \)
Therefore, the value of \( k \) is 12. Hence, the correct answer is option A.
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If sum of the squares of zeros of the quadratic polynomial f(x) = x2– 8x + k is 40, find the value of k.a)12b)-12c)14d)-14Correct answer is option 'A'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If sum of the squares of zeros of the quadratic polynomial f(x) = x2– 8x + k is 40, find the value of k.a)12b)-12c)14d)-14Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If sum of the squares of zeros of the quadratic polynomial f(x) = x2– 8x + k is 40, find the value of k.a)12b)-12c)14d)-14Correct answer is option 'A'. Can you explain this answer?.
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