Question

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and their coefficients.

$6x^2-x-1$

• A. $-\frac{1}{3},\frac{1}{2}$
• B. $-\frac{1}{4},\frac{1}{2}$
• C. $-\frac{1}{9},\frac{1}{7}$
• D. $-\frac{1}{3},\frac{1}{3}$

Answer 1

The correct option is A $-\frac{1}{3},\frac{1}{2}$

$6x^2-x-1$

$=6x^2-3x+2x-1$

$=3x(2x-1)+1(2x-1)$

$=(2x-1)(3x+1)$

$x=\frac{1}{2}$ , $x=-\frac{1}{3}$

The zeros of the polynomials are $\frac{1}{2}$ , $-\frac{1}{3}$

Relationship between the zeros and the coefficients of the polynomials-

Sum of the zeros=-$\frac{coefficientofx}{coefficientof{x}^2}=-\left(\frac{-1}{6}\right)=\frac{1}{6}$

Also sum of zeros = $\frac{1}{2}-\frac{1}{3}$ =$\frac{3-2}{6}$ =$\frac{1}{6}$

Product of the zeros =$\frac{constantterm}{coefficientof{x}^2}=\frac{-1}{6}$

Also the product of the zeros= $\left(\frac{1}{2}\right)\times (-\frac{1}{3})$ =$\frac{1}{6}$