Question

If α and β are zeroes of y² + 5y + m, find the value of m such that (α+β)² -αβ = 24.

Answer 1

Let α  and  β are  zeroes  of  the  polynomial  = y² +  5y +  m,

On comparing with ax²+bx+c=0
a= 1, b= 5, c = m

Sum of zeroes (α+β)= -b/a = -(5)/1
α+β= -5…………....(1)

Product of zeros(α.β)= c/a = m/1
α.β= c/a = m…………(2)

Given:  (α+β)² -αβ  = 24
(-5)² - m = 24
[From eq 1 & 2]
25 - m = 24
-m = 24 -25
-m = -1
m = 1

Hence, the value of m is 1.

HOPE THIS WILL HELP YOU...

Answer 2

the answer is -1
m=-1

i hope this will help u