Question

. Find the zeroes of the polynomials and verify the
relationship between zeroes and coefficients. The
polynomial is 2x2 + 3x + 1.​

Answer 1

Step-by-step explanation:

$Given \ polynomial,\\\implies 2x^2+3x+1 \\\\ =>2x^2+3x+1=0 \\2x^2+2x+x+1=0\\2x(x+1)+1(x+1)=0\\(2x+1)(x+1)=0\\=>2x+1=0;x=\frac{-1}{2} \\ =>x+1=0;x=-1 \\\\ \text{The zeroes of the polynomial are -1 and -1/2} \\\\ \underline{RELATIONSHIP \ BETWEEN \ ZEROES \ AND \ COEFFICIENTS} : \\\\ \rightarrow Sum \ of \ zeroes= -1+(\frac{-1}2}) =\frac{-3}{2} \\\\ Sum \ of \ zeroes=\frac{-x \ coefficient}{x^2 \ coefficient} \\\\ \rightarrow Product \ of \ zeroes=(-1)(\frac{-1}{2})=\frac{1}{2}$

$Product \ of \ zeroes=\frac{constant}{x^2 \ coefficient}$

Answer 2

2x^2+3x+1=0

2x^2 +2x+x+1=0

2x(x+1)+1(x+1)=0

(x+1) (2x+1)=0

There fore roots are (x+1) (2x+1)

Product of roots= c/a = 1/2

Sum of roots = -b/a = -3/1