Question

ax^2+bx+c=0
if alha square + beta square=25 and aplha -beta=1
find a b c​

Answer 1

Answer:

a=1

b=-7

c=12

Explanation:

Assuming the question meant that alpha and beta are the roots of the equation.

taking alpha =m and beta = n

we know m+n=-b/a

and mn=c/a

given m - n =1 and ,m^2+n^2=25

(m-n)^2=m^2+n^2 -2mn

1=25 - 2mn

2mn=24

mn=12

so c/a= 12

(m+n)^2=m^2+n^2+2mn

(m+n)^2=25+24

(m+n)^2=49

m+n=7

so -b/a=7

The quadratic can be written as x^2-(-b/a)x+(c/a)=0

x^2-7x+12=0

Comparing with ax^2+bx+c=0

a=1

b=-7

c=12