Question

find quadratic equation whose root are -3,7

Answer 1

let

α andβ are the roots

 soα = -3 and β = 7

general form of equation with α and β as roots  is[ x²-(α+β)x +αβ]  = 0 where k is constant

substituting the α and β values ,x²-(-3+7)x+(-3×7)

⇒x²-(4)x+(-21)= 0

x²-4x-21 = 0 is the quaquadratic equation whose root are  and -3 and 7

Answer 2

let 
α and β are the zeroes of the quadratic equation,
then the equation will be k[ax² -(α+β)x +αβ]
α = -3
β = 7
α+β = 4
αβ = -21
k[x² -(α+β)x +αβ] = k[x² -4x -21]

let k = 1
then the quadratic equation will be x² -4x -21 = 0