Find a quadratic equation whose roots are 2 and -5
Question
Find a quadratic equation whose roots are 2 and -5
Solution
A quadratic equation is given by the formula:
ax^2 + bx + c = 0
The roots of the equation are given by the formula:
x = [-b ± sqrt(b^2 - 4ac)] / 2a
Given that the roots of the equation are 2 and -5, we can form the equation as follows:
(x - 2)(x - (-5)) = 0
This simplifies to:
x^2 - 2x - 5x + 10 = 0
Which further simplifies to:
x^2 - 7x + 10 = 0
So, the quadratic equation whose roots are 2 and -5 is x^2 - 7x + 10 = 0.
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