Question

find the zero of the polynomial P/X =4x+5x-9and verify the relationship between the zero and it's coffiecent​

Answer 1

Step-by-step explanation:

In the given polynomial 4x2+9x+5,

The first term is 4x2 and its coefficient is 4.

The middle term is 9x and its coefficient is 9.

The last term is a constant term 5.

Multiply the coefficient of the first term by the constant 4×5=20.

We now find the factor of 20 whose sum equals the coefficient of the middle term, which is 9 and then factorize the polynomial 4x2+9x+5 and equate it to 0 as shown below:

 

4x2+9x+5=0⇒4x2+4x+5x+5=0⇒4x(x+1)+5(x+1)=0⇒(x+1)(4x+5)=0⇒(x+1)=0,(4x+5)=0⇒x=−1,4x=−5⇒x=−1,x=−45 

Hence, the zeroes of the polynomial 4x2+9x+5 are −1,−45.

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