Answer:
A
[tex]\frac{3 \pm\sqrt{17} }{-4}[/tex]
approx. 0.281, -1.781
B
(-18+-sqrt(204))/6
approx. -0.62, -5.38
Step-by-step explanation:
Finding The Zeroes in a Quadratic Function
In a quadratic function given as the general form:
[tex]ax^2 + bx +c=y[/tex]
the zeroes can be found using the formula:
[tex]x = \frac{-b \pm\sqrt{b^2-4ac} }{2a}[/tex]
a corresponds to the coefficient stuck to the squared variable,
b corresponds to the coefficient stuck to the standard variable
c corresponds to the constant
Problem Solving
In order to turn the given function into the general function, distribute everything correctly and put all values on one side of the equation so that the equation is equals to 0.
PART A
[tex]-2x(x+1.5)=-1[/tex]
[tex]-2x^2-3x=-1[/tex]
[tex]-2x^2-3x+1=0[/tex]
Now extract and solve for the zeroes according the formula given on top.
a = -2
b = -3
c = 1
[tex]\frac{-(-3) \pm\sqrt{(-3)^2-4(-2)(1)} }{2(-2)}[/tex]
[tex]\frac{-(-3) \pm\sqrt{9+8} }{-4}[/tex]
[tex]\frac{3 \pm\sqrt{17} }{-4}[/tex]
PART B
[tex]3x(x+6) =-10[/tex]
[tex]3x^2 + 18x=-10[/tex]
[tex]3x^2+18x+10=0[/tex]
Now extract and solve for the zeroes according the formula given on top.
a = 3
b = 18
c = 10
[tex]\frac{-18\pm\sqrt{18^2-4(3)(10)}}{2(3)}[/tex]
[tex]\frac{-18\pm\sqrt{324-120} }{6}[/tex]
[tex]\frac{-18\pm\sqrt{204} }{6}[/tex]
