The roots of x in the equation [tex]-10x^{2} + 12x - 9 = 0[/tex] is Option (B) [tex]\frac{3}{5}[/tex] ± [tex]\frac{3i\sqrt{6} }{10}[/tex]
What are the roots of an equation ?
The roots of quadratic equation are the values of the variable that satisfy the equation. They are also known as the solutions of the given quadratic equation.
What is quadratic equation formula ?
Suppose a quadratic equation is given as [tex]ax^{2} + bx + c = 0[/tex] .
The solution or roots of the equation is given as -
x = [tex]\frac{-b +- \sqrt{b^{2} - 4ac } }{2a}[/tex]
This formula is known as quadratic equation formula.
Finding the roots of the given equation -
Given quadratic equation is - [tex]-10x^{2} + 12x - 9 = 0[/tex]
We find the roots of the given equation by using the quadratic equation formula .
⇒ x = [tex]\frac{-12 +- \sqrt{12^{2} - 4(-10)(-9) } }{2(-10)}[/tex]
⇒ x = [tex]\frac{-12 +- \sqrt{144 - 360 } }{-20}[/tex]
⇒ x = [tex]\frac{-12 +- 6i\sqrt{6 } }{-20}[/tex]
⇒ x = [tex]\frac{-12}{-20}[/tex] ± [tex]\frac{-6i\sqrt{6} }{-20}[/tex]
∴ x = [tex]\frac{3}{5}[/tex] ± [tex]\frac{3i\sqrt{6} }{10}[/tex]
Thus, the roots of x in the equation [tex]-10x^{2} + 12x - 9 = 0[/tex] is Option (B) [tex]\frac{3}{5}[/tex] ± [tex]\frac{3i\sqrt{6} }{10}[/tex] .
To learn more about roots of an equation, refer -
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