Question

find the sum product of the zeros of p(×)×power2-5×-4

​

Answer 1

Step-by-step explanation:

In the given polynomial 4x

2

+12x+5,

The first term is 4x

2

and its coefficient is 4.

The middle term is 12x and its coefficient is 12.

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 12 and then factorize the polynomial 4x

2

+12x+5 and equate it to 0 as shown below:

4x

2

+12x+5=0

⇒4x

2

+2x+10x+5=0

⇒2x(2x+1)+5(2x+1)=0

⇒(2x+1)(2x+5)=0

⇒2x=−1,2x=−5

⇒x=−

2

1

,x=−

2

5

Therefore, the zeroes of the polynomial 4x

2

+12x+5 are −1,

3

4

.

Now, the sum and the product of the zeroes of the given quadratic polynomial is as follows:

−

2

1

+(−

2

5

)=−

2

1

−

2

5

=−

2

6

=−3

(−

2

1

)×(−

2

5

)=

2

1

×

2

5

=

4

5

Hence, the sum of the zeroes is −3 and the product of the zeroes is

4

5

.