Question

3.) Find the sum and
product of roots
of the quadratic
equation given
below.
3x2 + x + 1 = 0​

Answer 1

Answer:

Sum of the roots $=-\frac{b}{a} =-\frac{1}{3}$

product of the roots $=\frac{c}{a} =\frac{1}{3}$

Step-by-step explanation:

If a quadratic equation is given in standard form, we can find the sum and product of the roots using coefficient of $x^{2} ,x$ and constant term.

The standard form of a quadratic equation is

$ax^{2} +bx+c=0$

Here a, b, c are real and rational numbers.

Let α, β be two roots of the above quadratic equation

Then the formula to get sum and product of the roots of a quadratic equation is,

Sum of roots : $\alpha +\beta =-\frac{b}{a} =-\frac{coefficient of x}{coefficient of x^{2} }$

Product of roots :$\alpha \beta =\frac{c}{a}=\frac{x}{y} =\frac{constant term}{coefficient of x^{2} }$

comparing $3x^{2} +x+1=0$

and $ax^{2} +bx+c=0$

Here$a=3, b=1, c=1$

Therefore

Sum of the roots $=-\frac{b}{a} =-\frac{1}{3}$

product of the roots $=\frac{c}{a} =\frac{1}{3}$