Write the quadratic equation whose roots are -1 and -4 and whose leading coefficient is 1

The quadratic equation is y = x² + 5x + 4

Step-by-step explanation:

The form of the quadratic equation is y = ax + bx + c, where

∵ The leading coefficient of the quadratic equation is 1

∴ a = 1

∴ The equation is y = x² + bx + c

∵ Its roots are -1, -4

∴ Their sum = -1 + -4 = -5

∵ Their sum =

∴ -5 =

∴ -5 = -b

→ Multiply both sides by -1

∴ 5 = b

∵ The product of the roots = -4 × -1 = 4

∵ The product of the roots =

∴ 4 =

∴ 4 = c

→ Substitute the values of b and c in the equation above

∵ y = x² + 5x + 4

∴ The quadratic equation is y = x² + 5x + 4

45 minutes

step-by-step explanation:

a; x = 0.5

step-by-step explanation:

-10x = -5

x = 0.5