Find a quadratic equation with integer coefficients whose roots are 2 and7.
(x-2)(x-7)
multiply that out.
To find a quadratic equation with integer coefficients whose roots are 2 and 7, we can use the fact that the roots of a quadratic equation are represented as (x - root1)(x - root2) = 0.
In this case, the roots are 2 and 7. Plugging these values into the equation, we have:
(x - 2)(x - 7) = 0
Expanding and simplifying, we get:
x^2 - 2x - 7x + 14 = 0
Combining like terms, we have:
x^2 - 9x + 14 = 0
So, the quadratic equation with integer coefficients whose roots are 2 and 7 is:
x^2 - 9x + 14 = 0
To find a quadratic equation with integer coefficients whose roots are 2 and 7, we can utilize the fact that the roots of a quadratic equation in the form ax^2 + bx + c = 0 are given by the solutions of the equation.
The equation can be written as:
(x - 2)(x - 7) = 0
Expanding the equation:
x^2 - 2x - 7x + 14 = 0
x^2 - 9x + 14 = 0
So, the quadratic equation with integer coefficients whose roots are 2 and 7 is:
x^2 - 9x + 14 = 0