Question

Find the zeroes of the quadratic polynomial `x^2+7x+10 ,`and verify the relationship between the zeroes and the coefficients.

Answer 1

`P(x)=x^2+7x+10`
=`x^2+5x+2x+10`
=`x(x+5)+2(x+5)`
=`(x+2)(x+5)`
x=-2,-5
`alpha=-2,beta=-5`
`alpha+beta=-2-5=-7`
`alpha*beta=(-2)*(-5)=10`
`ax^2+bx+c`
a=1,b=7,c=10
`alpha+beta=-b/a=(-7)/1=-7`
`alpha*beta=c/a=10/1=10`