find the roots of the equation X(square)+7x equal to 0.(b)write down the equation whose roots are -2 and 5.
I will be happy to critique your thinking. Write the equation, and solve.
In the second, hint: (x+2) is one factor.
To find the roots of the equation X^2 + 7x = 0, we can solve it by factoring.
First, we identify the common factor in the equation, which is x. By factoring out x, we have:
x(x + 7) = 0
Now, we can set each factor equal to zero and solve for x:
x = 0 or x + 7 = 0
For the first equation, x = 0 is one of the roots.
For the second equation, we solve for x + 7:
x + 7 = 0
x = -7
So, the roots of the equation X^2 + 7x = 0 are x = 0 and x = -7.
Now, let's move on to the second part of the question. To write down an equation with roots -2 and 5, we can use the fact that if (x - a) is a factor of an equation, then x = a is a root.
So, if -2 is a root of the equation, then (x + 2) must be a factor. Similarly, if 5 is a root, then (x - 5) must be a factor.
Therefore, the equation with roots -2 and 5 is:
(x + 2)(x - 5) = 0
Expanding the equation, we get:
x^2 - 5x + 2x - 10 = 0
Simplifying further, we have:
x^2 - 3x - 10 = 0
Thus, the equation whose roots are -2 and 5 is x^2 - 3x - 10 = 0.