Question

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

Answer 1

Answer:

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

Step-by-step explanation:

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

• a is the leading coefficient

• Its roots are the values of x at y equal to zero

• The sum of the two roots is $-\frac{b}{a}$

• the product of the two roots is $\frac{c}{a}$

∵ 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 = $-\frac{b}{a}$

∴ -5 = $-\frac{b}{1}$

∴ -5 = -b

→ Multiply both sides by -1

∴ 5 = b

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

∵ The product of the roots = $\frac{c}{a}$

∴ 4 = $\frac{c}{1}$

∴ 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