[tex]x= \frac{10\pm \sqrt{40} }{6}[/tex] is the solution to the given quadratic equation.
What is quadratic equation?
Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = [tex]ax^{2} +bx+c[/tex] = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient and 'c' is called the absolute term of f (x).
Quadratic formula = [tex]\frac{-b\pm \sqrt{b^{2} -4ac} }{2a}[/tex]
Given quadratic equation
[tex]3x^{2} -10x+5=0[/tex]
a = 3, b = -10, c = 5
Quadratic formula = [tex]\frac{-b\pm \sqrt{b^{2} -4ac} }{2a}[/tex]
[tex]x= \frac{-(-10)\pm \sqrt{(-10)^{2} -4(3)(5)} }{2\times3}[/tex]
⇒ [tex]x= \frac{10\pm \sqrt{100 -60} }{6}[/tex]
⇒ [tex]x= \frac{10\pm \sqrt{40} }{6}[/tex]
Hence, [tex]x= \frac{10\pm \sqrt{40} }{6}[/tex] is the solution to the given quadratic equation.
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