If x + 3 is a factor of P(x) = x3 + ax2 - 7x + 6 , then find a
Answers
a = 14/3
Step-by-step explanation:
When we say that something is factor of a function. This means when we put that value in the place of variable e.g. "x" here, it should satisfy the function or in other words the answer should be equal to zero.
Such as
X + 3 = 0, X = -3
Now, putting X = -3 in the place of "X" in the function,we get
(-3)^3 + a (-3)^2 -7 (-3) + 6 = 0
-27 + a 9 -15= 0
9 a = 42
a = 14/3
Given : x + 3 is a factor of f P(x) = x³ + ax² - 7x + 6
To find : Value of a
Solution:
x + 3 is a factor of f P(x) = x³ + ax² - 7x + 6
=> x = - 3
=> P(-3) = 0
putting x = - 3 & equating with zero
=> (-3)³ + a(-3)² -7(-3) + 6 = 0
=> -27 -9a + 21 + 6 = 0
=> -27 - 9a + 27 = 0
=> -9a = 0
=> a = 0
a = 0 if x + 3 is a factor of P(x) = x³ + ax² - 7x + 6
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