Final answer:
The quadratic equation y²-10y+24=0 can be factored to find its solutions, which are 4 and 6.
Step-by-step explanation:
The equation y²-10y+24=0 is a quadratic equation, which can be solved for y using the quadratic formula. However, we can also factor this equation directly since the coefficients are relatively simple. To factor the equation, we need to find two numbers that multiply to give us 24 (the constant term) and add up to -10 (the coefficient of the middle term yo). These two numbers are -4 and -6. Thus, the equation factors to:
(y - 4)(y - 6) = 0
Setting each factor equal to zero gives us the solutions for y:
- y - 4 = 0 ⇒ y = 4
- y - 6 = 0 ⇒ y = 6
So, the two solutions to the equation are 4 and 6.