Question

If alfa and beeta are the zeros of the polynomial x2-8x+m such that alfa2+beeta2=40 find the value of m

Answer 1

hello users ......

we have given that :-
α and β are the roots of quadratic equation :x² - 8x + m = 0 

Such that :
α² + β² = 40 

we have to find 
m = ? 

solution :-

we know that : 
For a quadratic equation : ax² + bx + c = 0

sum of roots = - b / a ;
and
product of roots = c / a 

here;
sum of roots = α + β = - b / a = -(-8) / 1 = 8 
and
product of roots = αβ = c / a = m / 1 = m 

now , we know that :
a² + b² = (a + b)² - 2 ab 

here;
α² + β² = ( α + β )² - 2 αβ

=> 40 = 8² - 2 × m 

=> 2m = 64 - 40 

=> 2m = 24 

=> m = 12 answer .

✰✰ hope it helps ✰✰