Question

Find the sum of roots ofof given quadratic equation ofx2 – 3x – 10 = 0

Answer 1

Answer:

$\sf \longrightarrow \alpha +\beta = 3$

Step-by-step explanation:

Given :

$\sf x^2-3x-10=0$

We are asked to find sum of zeroes :

$\sf \longrightarrow x^2-3x-10=0$

$\sf \longrightarrow x^2-5x+2x-10=0$

$\sf \longrightarrow x(x-5)+2(x-5)=0$

$\sf \longrightarrow (x+2)(x-5)=0$

Now zeroes :

$\sf \longrightarrow (x+2)=0$

$\sf x=-2$

OR

$\sf \longrightarrow (x-5)=0$

$\sf x =5$

Now sum :

$\sf \alpha +\beta =5-2$

$\sf \alpha +\beta =3$

Alternate method :

We know if :

$\sf ax^2+bx+c=0 \ ,a\neq 0$

$\displaystyle \text{{Sum of zeroes : }}$

$\sf \implies - \dfrac{b}{a}$

$\sf \longrightarrow \alpha +\beta =-\dfrac{-3}{1}$

$\sf \longrightarrow \alpha +\beta = 3$

Hence we get required answer.