Question

find alpha+betha and alpha ×beta​

Answer 1

Answer:

first we need to know value of alpha + beta and alpha × beta :-

Let's consider the equation = ax^2 + bx + c = 0

From the given equation in question i.e 5x^2 +6X+1=0

a=5, b=6,c=1

Using the quadratic formula,

Alpha + Beta = -b/a

Now, putting the value

=> Alpha + Beta = -6/5

Alpha * Beta = c/a

=> Alpha * Beta = 1/5

now, How do you find alpha and beta :-

1. If the quadratic equation ax2+bx+c=0 , has roots αandβ, then α+β=−baandα⋅β=ca. Here,
2. x2−22x+105=0⇒a=1,b=−22,c=105.
3. So, α+β=−−221=22,andαβ=1051=105. Now, (α−β)=√(α+β)2−4αβ ,... where,(α>β)
4. (α−β)=√(22)2−4(105)
5. (α−β)=√484−420=√64=8.