write sum and product of zero of polynomial 12x^3-4x²-3x+
Answers
Step-by-step explanation:
In the given polynomial 4x2+12x+5,
The first term is 4x2 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 4x2+12x+5 and equate it to 0 as shown below:
4x2+12x+5=0⇒4x2+2x+10x+5=0⇒2x(2x+1)+5(2x+1)=0⇒(2x+1)(2x+5)=0⇒2x=−1,2x=−5⇒x=−21,x=−25
Therefore, the zeroes of the polynomial 4x2+12x+5 are −1,34.
Now, the sum and the product of the zeroes of the given quadratic polynomial is as follows:
=》 -1/2+(-5/2)= -1/2 -5/2= -6/2= -3
=》(-1/2)×(-5/2)=1/2×5/2= 5/4
=》Hence, the sum of the zeros is -3 and the product of zeros is 5/4.