Answer:
The roots of the quadratic equation are.
t = -0.78
t = -4.62
Step-by-step explanation:
Assume: we find the roots of the given quadratic equation.
Given:
the given expression is.
T squared plus 5.4t plus 3.6 equals 0
Rewrite the equation as.
[tex]t^{2}+5.4t+3.6=0[/tex]
Now, we first find the root of the above equation.
Use quadratic formula with [tex]a=1, b=5.4, c=3.6[/tex].
[tex]t=\frac{-b\pm \sqrt{(b)^{2}-4ac}}{2a}[/tex]
Put a, b and c value in above equation.
[tex]t=\frac{-5.4\pm \sqrt{(5.4)^{2}-4(1)(3.6)}}{2(1)}[/tex]
[tex]t=\frac{-5.4\pm \sqrt{29.16-4\times 3.6}}{2}[/tex]
[tex]t=\frac{-5.4\pm \sqrt{29.16-14.4}}{2}[/tex]
[tex]t=\frac{-5.4\pm \sqrt{14.76}}{2}[/tex]
[tex]t=\frac{-5.4\pm 3.84}{2}[/tex]
For positive sign
[tex]t=\frac{-5.4 + 3.84}{2}[/tex]
[tex]t=\frac{-1.56}{2}[/tex]
t = -0.78
For negative sign
[tex]t=\frac{-5.4 - 3.84}{2}[/tex]
[tex]t=\frac{-9.24}{2}[/tex]
t = -4.62
Therefore the roots of the quadratic equation t = -0.78 or t = -4.62
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