Question

write the sum and the product of the roots of 2 X square + 10 x minus 5 equals to zero

Answer 1

p(x)=2x²+10x-5=0

let a and b the zeroes of the given polynomial

a+b=(-b)/a

a+b=-(10)/2

a+b=-5

ab=c/a

ab=-5/2

hope this helps u

Answer 2

$\alpha+\beta=-5$

$\alpha \beta=-\frac{5}{2}$

Step-by-step explanation:

Given : Quadratic equation $2x^2+10x-5=0$

To find : Write the sum and the product of the roots of  equation ?

Solution :

The sum of and product of quadratic equation $ax^2+bx+c=0$ with roots $\alpha$ and $\beta$ is given by,

The sum of roots is  $\alpha+\beta=-\frac{b}{a}$

The product of roots is  $\alpha \beta=\frac{c}{a}$

In $2x^2+10x-5=0$, a=2, b=10 and c=-5

Substitute the values,

The sum of roots is  $\alpha+\beta=-\frac{b}{a}$

$\alpha+\beta=-\frac{10}{2}$

$\alpha+\beta=-5$

The product of roots is  $\alpha \beta=\frac{c}{a}$

$\alpha \beta=\frac{-5}{2}$

$\alpha \beta=-\frac{5}{2}$

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