The zeros of the given quadratic functions are x₁ = -2.05 and x₂ = 14.61
The complete question is given below:-
Y=-6x²+100x-180 What are the zeroes of the function? Round to the nearest hundredth.
What is a quadratic equation?
The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.
Use the quadratic formula to solve it:
Y= -6x² +100x -180
a= -6
b= 100
c= -180
x =[tex]\dfrac{ -b \pm \sqrt{(b^2 - 4ac)} }{ 2a}[/tex]
x =[tex]\dfrac{-100 \pm \sqrt {(10,000 -4*-6*-180)}}{ -12}[/tex]
x1 =[tex]\dfrac{ (-100 + 75.3658 )} { -12}[/tex]
x1 = 24.6342 / -12
x1 = -2.05285
x2 =[tex]\dfrac{ (-100 - 75.3658 )} { -12}[/tex]
x2 = (- 175.3658 ) / -12
x 2 = 14.6138
Therefore the zeros of the given quadratic functions are x₁ = -2.05 and x₂ = 14.61
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