if a and b are the roots of the quadratic equation x^2+4x-k=0 and a>b, find the value of a-b
+118703 if a and b are the roots of the quadratic equation x^2+4x-k=0 and a>b, find the value of a-b
[I have replace a with α and b with β because I wanted a and be to stand for the quadratic coefficients]
For the quadratic
ax2+bx+c=0Iftherootsareαandβthenα+β=−baandα+β=ca
α+β=−4αβ=−k(α+β)2−4αβ=α2+β2+2αβ−4αβ=α2+β2−2αβ=(α−β)2so(α−β)2=(α+β)2−4αβ(α−β)2=(−4)2−4∗−k(α−β)2=16+4kα−β=±√16+4kButαisbiggerthanβsoα−β=√16+4kα−β=2√4+k
+26396 If a and b are the roots of the quadratic equation x^2+4x-k=0 and a>b, find the value of a-b
x1,2=−4±√16−4∗(−k)2=−4±√16+4k2=−4±√4(4+k)2 x1,2=−4±2√4+k2=−2±√4+k a=−2+√4+k|a>b b=−2−√4+k a−b=−2+√4+k−(−2−√4+k)=−2+√4+k+2+√4+k)=2√4+k a−b=2√4+k
+118703 if a and b are the roots of the quadratic equation x^2+4x-k=0 and a>b, find the value of a-b
[I have replace a with α and b with β because I wanted a and be to stand for the quadratic coefficients]
For the quadratic
ax2+bx+c=0Iftherootsareαandβthenα+β=−baandα+β=ca
α+β=−4αβ=−k(α+β)2−4αβ=α2+β2+2αβ−4αβ=α2+β2−2αβ=(α−β)2so(α−β)2=(α+β)2−4αβ(α−β)2=(−4)2−4∗−k(α−β)2=16+4kα−β=±√16+4kButαisbiggerthanβsoα−β=√16+4kα−β=2√4+k
