Class 9 Exam > Class 9 Questions > x-a is a factor of p(x)= ax2+bx+c. Which of t...
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x-a is a factor of p(x)= ax2+bx+c. Which of the following is true?
- a)p(a)=2
- b)p(a) = 0
- c)p(2)=1
- d)p(b)=0
Correct answer is 'B'. Can you explain this answer?
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Verified Answer
x-a is a factor of p(x)= ax2+bx+c. Which of the following is true?R...
See if g(x) = x- a
Then g(x) is a factor of p(x)
The zero of polynomial = a
Therefore p(a)= 0
Then g(x) is a factor of p(x)
The zero of polynomial = a
Therefore p(a)= 0
Most Upvoted Answer
x-a is a factor of p(x)= ax2+bx+c. Which of the following is true?R...
To prove that option B is correct, we need to show that p(a) = 0.
Given that x - a is a factor of p(x) = ax^2 + bx + c, we can write p(x) as:
p(x) = (x - a)(mx + n)
Where m and n are constants.
Expanding the equation, we get:
p(x) = (x - a)(mx + n) = mx^2 + (n - am)x - an
Now, we need to find the value of p(a).
Substituting x = a in the equation, we get:
p(a) = ma^2 + (n - am)a - an = ma^2 + na - a^2m - an = ma^2 - a^2m + na - an
We can factor out 'a' from the equation:
p(a) = a(ma - am) + na - an = a(0) + na - an = na - an = n(a - 1)
Since (x - a) is a factor of p(x), it implies that when x = a, p(x) = 0. Therefore, p(a) = 0.
So, option B is true: p(a) = 0.
Given that x - a is a factor of p(x) = ax^2 + bx + c, we can write p(x) as:
p(x) = (x - a)(mx + n)
Where m and n are constants.
Expanding the equation, we get:
p(x) = (x - a)(mx + n) = mx^2 + (n - am)x - an
Now, we need to find the value of p(a).
Substituting x = a in the equation, we get:
p(a) = ma^2 + (n - am)a - an = ma^2 + na - a^2m - an = ma^2 - a^2m + na - an
We can factor out 'a' from the equation:
p(a) = a(ma - am) + na - an = a(0) + na - an = na - an = n(a - 1)
Since (x - a) is a factor of p(x), it implies that when x = a, p(x) = 0. Therefore, p(a) = 0.
So, option B is true: p(a) = 0.
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Community Answer
x-a is a factor of p(x)= ax2+bx+c. Which of the following is true?R...
Since ,x-a is a factor of P(x)..so,x-a=0.. i.e.x=a... so,we can say a is the zero of P(x)..so,P(a)=0...
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x-a is a factor of p(x)= ax2+bx+c. Which of the following is true?a)p(a)=2b)p(a) = 0c)p(2)=1d)p(b)=0Correct answer is 'B'. Can you explain this answer?
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