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If one of the zeros of quadratic polynomial (k-1)x2 + kx + 1 is -3 then the value of k?
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If one of the zeros of quadratic polynomial (k-1)x2 + kx + 1 is -3 the...
To find the value of \( k \) for which one of the zeros of the quadratic polynomial \((k-1)x^2 + kx + 1\) is \(-3\), we can follow these steps:
Step 1: Substitute the zero into the polynomial
- We know that if \(-3\) is a zero, then substituting \(-3\) into the polynomial must yield zero:
\[
(k-1)(-3)^2 + k(-3) + 1 = 0
\]
Step 2: Simplify the equation
- Now, simplify the equation:
- Calculate \((-3)^2\):
\[
9(k-1) - 3k + 1 = 0
\]
- Expand and combine like terms:
\[
9k - 9 - 3k + 1 = 0
\]
\[
6k - 8 = 0
\]
Step 3: Solve for \( k \)
- Rearranging the equation gives:
\[
6k = 8
\]
\[
k = \frac{8}{6} = \frac{4}{3}
\]
Conclusion
- Therefore, the value of \( k \) such that one of the zeros of the polynomial is \(-3\) is:
\[
k = \frac{4}{3}
\]
This process shows how substituting a known zero into the polynomial leads to determining the required parameter \( k \).
Step 1: Substitute the zero into the polynomial
- We know that if \(-3\) is a zero, then substituting \(-3\) into the polynomial must yield zero:
\[
(k-1)(-3)^2 + k(-3) + 1 = 0
\]
Step 2: Simplify the equation
- Now, simplify the equation:
- Calculate \((-3)^2\):
\[
9(k-1) - 3k + 1 = 0
\]
- Expand and combine like terms:
\[
9k - 9 - 3k + 1 = 0
\]
\[
6k - 8 = 0
\]
Step 3: Solve for \( k \)
- Rearranging the equation gives:
\[
6k = 8
\]
\[
k = \frac{8}{6} = \frac{4}{3}
\]
Conclusion
- Therefore, the value of \( k \) such that one of the zeros of the polynomial is \(-3\) is:
\[
k = \frac{4}{3}
\]
This process shows how substituting a known zero into the polynomial leads to determining the required parameter \( k \).
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If one of the zeros of quadratic polynomial (k-1)x2 + kx + 1 is -3 then the value of k?
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If one of the zeros of quadratic polynomial (k-1)x2 + kx + 1 is -3 then the value of k? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If one of the zeros of quadratic polynomial (k-1)x2 + kx + 1 is -3 then the value of k? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If one of the zeros of quadratic polynomial (k-1)x2 + kx + 1 is -3 then the value of k?.
If one of the zeros of quadratic polynomial (k-1)x2 + kx + 1 is -3 then the value of k? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If one of the zeros of quadratic polynomial (k-1)x2 + kx + 1 is -3 then the value of k? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If one of the zeros of quadratic polynomial (k-1)x2 + kx + 1 is -3 then the value of k?.
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