Question

if alpha = 5+2√2 and Beta = 5-2√2 then find the value of k​

Answer 1

Answer:

Let us assume the quadratic equation to be of the form ax2+bx+c=0

Given that α and β are the roots of this equation,

Sum of the roots = α+β=−b/a=−3=−6/2

Product of the roots = αβ=c/a=−5/2

Now ax2+bx+c=0 can be written as x2+(b/a)x+c/a=0, on dividing throughout by a.

Now, + (b/a)x can be written as −(−b)x/a .

Substituting the known values we get,

x2−(−6/2)x+(−5/2)=0

Multiplying throughout by 2, we get the quadratic equation, 2x2+6x−5=0.