The correct option is A x2+7x+12=0
Given: x2−7x+12=0 with roots α,β
To find: Quadratic equation with roots −α,−β
Sum of roots α+β=−ba=−−71=7
Product of roots α⋅β=ca=121=12
Now, quadratic equation with roots −α,−β will be given as:
x2−(−α−β)x+(−α)(−β)=0
⇒x2+(α+β)x+α.β=0
⇒x2+7x+12=0
Hence, quadratic equations with roots −α,−β is x2+7x+12=0