Grade 10 Exam > Grade 10 Questions > If the polynomial f(x) = x2+ kx - 15, is exac...
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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?
Verified 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
Most Upvoted 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.
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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?
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