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CGP EDU Academic Team
Published on: August 13, 2026
Let P (x) = x 2 + bx + c, where b and c are integers. If P(x) is a factor of both x 4 + 6x 2 +25 and 3x 2 + 4x 2 + 28x + 5, then the value of P(1) is
Text Solution
Verified by ExpertsThe correct answer is:
4
(4)
Sol. If x = 
is the common root of both the equations, then
4 + 6 
2 + 25 = 0 
4 = -25 - 6 
2 Using this value of 
4 in the second equation
3 (-25 - 6 
2 ) + 4 
2 + 28 
+ 5 = 0
-75 - 18 
2 + 4 
2 + 28 
+ 5 = 0
2 
2 - 4 
+ 10 = 0
2 - 2 
+ 5 = 0
on comparing with x 2 + bx + c, we get
b = -2, c = 5
So, P (x) = x 2 - 2x + 5
P(l) = (-1) - 2 + 5 = 4
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