Question

Quadratic equation whose roots are 1 and -1/2

Answer 1

Given:

roots are 1 and -1/2

To find:

Quadratic equation=?

Solution:

The formula of Quadratic equation:

$\bold{x^2 - (sum \ of \ roots) x + \ Product \ of \ roots = 0}$

roots:

$\alpha = 1\\\\\beta= -\frac{1}{2}$

The sum of roots:

$\to {\alpha +\beta} \\\\\to 1+(-\frac{1}{2})\\\\\to 1-\frac{1}{2}\\\\\to \frac{2-1}{2}\\\\\to \frac{1}{2}$

The product of roots:

$\to \alpha \times \beta\\\\\to 1 \times (-\frac{1}{2})\\\\\to -\frac{1}{2}$

Quadratic equation:

$\to x^2-(\frac{1}{2})x+ (-\frac{1}{2})=0\\\\\to \frac{2x^2-x-1}{2}=0\\\\\to \boxed{2x^2-x-1=0}$