Question

Find thezeroes of the following quadratic polynomials abd verify the relationship
between the zeroes and the coefficients : -1 + 3x + 10x^2

Answer 1

SOLUTION☺

Let f(x)= 10x^2+3x-1 and alpha and beta be it's zeroes

Here, a= 10, b= 3, c= -1

=) 10x^2+3x-1=0

=) 10x^2+(5-2)x-1=0

=) 10x^2+5x-2x-1=0

=) 10x(x+5)-2(x+5) =0

=)(x+5) (10x-2)=0

=) x+5= 0 or 10x-2=0

=) x= -5 or 10x= 2

=) x= 5 or x= 2/10 = 1/5

Now,

Alpha+ beta= 5+ 1/5= 25+1/5

=) 26/5 = - coefficient of x/coefficient of x^2

Aplha.beta= 5× 1/5= 1 = coefficient term/cofficient of x^2

hope it helps