Grade 10 Exam > Grade 10 Questions > If the polynomial f(x) = x2+ kx - 15, is exac...
Start Learning for Free
If the polynomial f(x) = x2 + kx - 15, is exactly divisible by x - 5, then the value of k is _______
- a)3
- b)2
- c)-3
- d)-2
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
If the polynomial f(x) = x2+ kx - 15, is exactly divisible by x - 5, t...
x2 + kx - 15 is exactly divisible by x - 5
Dividing, x2 + kx + 15 by x - 5
We get, 5k + 10 as remainder.
Since, x2 + kx - 15 is exactly divisible by 2x - 5
∴ 5k + 10 = 0
k = -2
Dividing, x2 + kx + 15 by x - 5
We get, 5k + 10 as remainder.
Since, x2 + kx - 15 is exactly divisible by 2x - 5
∴ 5k + 10 = 0
k = -2
Free Test
FREE
| Start Free Test |
Community Answer
If the polynomial f(x) = x2+ kx - 15, is exactly divisible by x - 5, t...
To determine the value of k in the polynomial f(x) = x^2 + kx - 15, we need to find the value of k such that the polynomial is exactly divisible by x - 5.
To check if the polynomial is divisible by x - 5, we can use the Remainder Theorem, which states that if a polynomial f(x) is divided by x - a, the remainder is equal to f(a).
Let's substitute x = 5 into the polynomial f(x) and check if the remainder is equal to zero.
f(5) = 5^2 + 5k - 15
= 25 + 5k - 15
= 5k + 10
For the polynomial to be exactly divisible by x - 5, the remainder should be zero. Therefore, we need to find the value of k that makes 5k + 10 = 0.
Solving the equation 5k + 10 = 0 for k gives us k = -2.
Therefore, the value of k that makes the polynomial f(x) = x^2 + kx - 15 exactly divisible by x - 5 is k = -2.
Hence, the correct answer is option D) -2.
To check if the polynomial is divisible by x - 5, we can use the Remainder Theorem, which states that if a polynomial f(x) is divided by x - a, the remainder is equal to f(a).
Let's substitute x = 5 into the polynomial f(x) and check if the remainder is equal to zero.
f(5) = 5^2 + 5k - 15
= 25 + 5k - 15
= 5k + 10
For the polynomial to be exactly divisible by x - 5, the remainder should be zero. Therefore, we need to find the value of k that makes 5k + 10 = 0.
Solving the equation 5k + 10 = 0 for k gives us k = -2.
Therefore, the value of k that makes the polynomial f(x) = x^2 + kx - 15 exactly divisible by x - 5 is k = -2.
Hence, the correct answer is option D) -2.
Attention Grade 10 Students!
To make sure you are not studying endlessly, EduRev has designed Grade 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Grade 10.
|
Explore Courses for Grade 10 exam
|
|
Similar Grade 10 Doubts
Top Courses for Grade 10View all
If the polynomial f(x) = x2+ kx - 15, is exactly divisible by x - 5, then the value of k is _______a)3b)2c)-3d)-2Correct answer is option 'D'. Can you explain this answer?
Question Description
If the polynomial f(x) = x2+ kx - 15, is exactly divisible by x - 5, then the value of k is _______a)3b)2c)-3d)-2Correct answer is option 'D'. Can you explain this answer? for Grade 10 2024 is part of Grade 10 preparation. The Question and answers have been prepared according to the Grade 10 exam syllabus. Information about If the polynomial f(x) = x2+ kx - 15, is exactly divisible by x - 5, then the value of k is _______a)3b)2c)-3d)-2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Grade 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the polynomial f(x) = x2+ kx - 15, is exactly divisible by x - 5, then the value of k is _______a)3b)2c)-3d)-2Correct answer is option 'D'. Can you explain this answer?.
If the polynomial f(x) = x2+ kx - 15, is exactly divisible by x - 5, then the value of k is _______a)3b)2c)-3d)-2Correct answer is option 'D'. Can you explain this answer? for Grade 10 2024 is part of Grade 10 preparation. The Question and answers have been prepared according to the Grade 10 exam syllabus. Information about If the polynomial f(x) = x2+ kx - 15, is exactly divisible by x - 5, then the value of k is _______a)3b)2c)-3d)-2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Grade 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the polynomial f(x) = x2+ kx - 15, is exactly divisible by x - 5, then the value of k is _______a)3b)2c)-3d)-2Correct answer is option 'D'. Can you explain this answer?.
Solutions for If the polynomial f(x) = x2+ kx - 15, is exactly divisible by x - 5, then the value of k is _______a)3b)2c)-3d)-2Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Grade 10.
Download more important topics, notes, lectures and mock test series for Grade 10 Exam by signing up for free.
Here you can find the meaning of If the polynomial f(x) = x2+ kx - 15, is exactly divisible by x - 5, then the value of k is _______a)3b)2c)-3d)-2Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If the polynomial f(x) = x2+ kx - 15, is exactly divisible by x - 5, then the value of k is _______a)3b)2c)-3d)-2Correct answer is option 'D'. Can you explain this answer?, a detailed solution for If the polynomial f(x) = x2+ kx - 15, is exactly divisible by x - 5, then the value of k is _______a)3b)2c)-3d)-2Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of If the polynomial f(x) = x2+ kx - 15, is exactly divisible by x - 5, then the value of k is _______a)3b)2c)-3d)-2Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If the polynomial f(x) = x2+ kx - 15, is exactly divisible by x - 5, then the value of k is _______a)3b)2c)-3d)-2Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Grade 10 tests.
|
|
Explore Courses for Grade 10 exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup