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Maths-

General

Easy

Question

ax³ + bx² + cx + d = 0
In the equation above, a, b, c, and d are constants. If the equation has roots −1, −3, and 5, which of the following is a factor of ax³ + bx² + cx + d = 0

x − 1
x + 1
x − 3
x + 5

The correct answer is: x + 1

HINT – If f(a) = 0, then ( x – a) is a factor of the given polynomial
SOLUTION - Roots of the equation are – 1 , - 3 , 5
$rightwards double arrow$ x = - 1 , - 3 and 5 satisfies the given cubic polynomial
$rightwards double arrow$ f( - 1) = 0 , f( - 3) = 0 and f( 5 ) = 0
We know that if f(a) = 0 then ( x – a ) is a factor of the given polynomial
i.e. (x – (-1)) , (x – (-3)) and (x – 5) are the factors
$rightwards double arrow$ ( x + 1) , ( x + 3) and (x – 5) are the factors of the given p polynomial.
Hence, option B is correct

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