How do I write an quadratic equation whose roots are -1 and -2 and whose leading coefficient is 1. Sorry my equal key does not work
blank equals 0
x = -1
x+1 = 0
x = -2
x+2 = 0
(x+1)(x+2) = 0
x^2 + 2x + x + 2 = 0
x^2 + 3x + 2 = 0
How do I write the quadratic equation whose root are 3 and -6 and whose leading coefficient is 1
No problem. To write a quadratic equation with roots -1 and -2, we can use the fact that the quadratic equation is in the form:
(x - r₁)(x - r₂) = 0
where r₁ and r₂ are the roots of the equation. In this case, r₁ = -1 and r₂ = -2.
So, substituting the given values in the equation:
(x - (-1))(x - (-2)) = 0
Simplifying further:
(x + 1)(x + 2) = 0
Now, if you want to write the equation in standard form with a leading coefficient of 1, we can multiply both sides of the equation by 1 to simplify:
1 * (x + 1)(x + 2) = 0
Expanding the equation:
(x + 1)(x + 2) = 0
(x + 1)(x) + (x + 1)(2) = 0
x(x) + x(1) + 2(x) + 2(1) = 0
x² + x + 2x + 2 = 0
Combining like terms:
x² + 3x + 2 = 0
Therefore, the quadratic equation with roots -1 and -2 and a leading coefficient of 1 is:
x² + 3x + 2 = 0