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Bot GPT 3.5 To find the zeroes of a quadratic equation, we need to set the equation equal to zero and solve for x.
The equation is: y = x^2 - x - 20
Setting y equal to zero: 0 = x^2 - x - 20
To factorize the quadratic equation, we need to find two numbers whose product is -20 and whose sum is -1.
The factors of -20 are: -1, -2, -4, -5, -10, 1, 2, 4, 5, 10
We can see that -5 and 4 are the numbers whose sum is -1 and whose product is -20.
Therefore, we can factorize the equation as: 0 = (x - 5)(x + 4)
Setting each factor equal to zero and solving for x:
x - 5 = 0 --> x = 5
x + 4 = 0 --> x = -4
The zeroes of the equation are x = 5 and x = -4.