Question one how many solutions or zeros does the equation y = x2 + 6x + 9/2 question two select all the correct solutions to 0 equals x2 + 7x - 30 is it a x equals 7 bx = 3 c x equals -10 d x equals -3.5 or e x = -30
Question one:
The equation y = x^2 + 6x + 9/2 can be simplified to y = x^2 + 6x + 4.5. To find the number of solutions or zeros, we can determine the discriminant of the quadratic equation. The discriminant is given by b^2 - 4ac, where a, b, and c are the coefficients of the equation.
In this case, a = 1, b = 6, and c = 4.5. Plugging these values into the discriminant formula, we get:
Discriminant = 6^2 - 4(1)(4.5) = 36 - 18 = 18.
Since the discriminant (18) is positive, the quadratic equation has 2 distinct solutions or zeros.
Question two:
The given equation is 0 = x^2 + 7x - 30.
To find the correct solutions, we need to factorize the quadratic equation. Factoring, we get:
0 = (x - 3)(x + 10).
From this, we can see that the correct solutions are:
- x = 3 (option b)
- x = -10 (option c)
The solutions x = 7 (option a) and x = -30 (option e) are not correct.