Question

What multiplies into -3 and adds to 11

Answer 1

x^2 + 11x - 3

What two numbers multiply to -3 and add to 11?

Let's use the quadratic equation:


`x = (-b\pm √(b^2-4ac))/(2a)`

Where the equation is ax^2 + bx + c


`x = (-11\pm √(11^2-4(1)(-3)))/(2(1))\\\\x = (-11\pm √(121+12))/(2)\\\\x = (-11\pm √(133))/(2)\\\\ \boxed{\bf{x = -(11)/(2) + (√(133))/(2)}}\\\\ \boxed{\bf{x = -(11)/(2) - (√(133))/(2)}}`

The two boxed values are what multiply to -3 and add to 11.