Question

2. The sum of the zeroes of the quadratic polynomial p (x) = x + 5x + 4 is greater than the product of its zeroes.​

Answer 1

Given :

A quadratic polynomial $p(x)=x^{2} +5x+4$

To prove :

The sum of the zeroes of the quadratic polynomial is greater than the product of its zeroes.​

Step-by-step explanation:

• The zeroes can be found by using splitting the middle term.
• First of all, multiply the co efficient of $x^{2}$ with the constant.
• Secondly, the middle term must be separated in such a way that the product of the terms must lead to the co product of 1st and 3rd term.
• Thirdly, the addition of separated middle term must lead to the co efficient of the 2nd term.
• By using splitting the middle term we get,

       $x^{2} +4x+x+4$

• Take x as common from $x$ which will lead to

       $x(x+4)+1(x+4)$

• By taking $(x+4)$ as common.
• The terms would be

       $(x+4)(x+1)$

• The zeroes can be calculated by equating the terms to 0.

       $x=4 , x=1$

• The sum of zeroes would be

       $4+1=5$

• The product of zeroes would be

       $(4)(1)=4$

• The sum of zeroes is 4 whereas product of zeroes is 4.
• Therefore, sum of zeroes is greater than the product of zeroes in this case of quadratic polynomial.

Final answer :

sum of zeroes is greater than the product of zeroes in $p(X)=x^{2} +5x+4$