A quadratic equation is an equation whose leading coefficient is of the second degree. The correct option is C.
What is a quadratic equation?
A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.
How to find the roots of a quadratic equation?
Suppose that the given quadratic equation is
ax²+bx+c
Then its roots are given as:
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
The solution of a quadratic equation is the root of the equation. Therefore, the roots of the given equation 2x² - 12x - 50 = 0 is,
2x² - 12x - 50 = 0
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\\\x = \dfrac{-(-12) \pm \sqrt{(-12)^2 - 4(2)(-50)}}{2(2)}[/tex]
x = 3±√34
A.)
(x-6)² = 31
(x-6) = ± √31
x = 6 ± √31
B.)
(x-3)² = 16
(x-3) = ± √16
(x-3) = ± 4
x = 3 ± 4
x = -1, 7
C.)
(x-3)² = 34
(x-3) = ± √34
(x-3) = ± √34
x = 3 ± √34
x = 3 ± √34
D.)
(x-6)² = 19
(x-6) = ± √19
x = 6 ± √19
Hence, the equation that has the same solution as 2x² - 12x - 50 = 0 is (x-3)² = 34.
Learn more about Quadratic Equations:
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