Question

3) Solve each equation using the quadratic formula. Show
a. x2 – 3x – 10 = 0

Answer 1

x = -2 or x = 5

Explanation:

The quadratic formula of a quadratic equation

`ax^2+bx+c=0\\\\\text{If}\ b^2-4ac>0\ \text{then the equation has two solutions}\ x=(-b\pm√(b^2-4ac))/(2a)`

`\text{If}\ b^2-4ac=0\ \text{then the equation has one solution}\ x=(-b)/(2a)`

`\text{If}\ b^2-4ac<0\ \text{then the equation has no solution}`

We have:

`x^2-3x-10=0\to a=1,\ b=-3,\ c=-10\\\\b^2-4ac=(-3)^2-4(1)(-10)=9+40=49>0\\\\x=(-(-3)\pm√(49))/(2(1))=(3\pm7)/(2)\\\\x=(3-7)/(2)=(-4)/(2)=-2\\or\\x=(3+7)/(2)=(10)/(2)=5`