A quadratic equation is an equation whose leading coefficient is of the second degree. The correct option is D.
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.
Its roots are given as:
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
A.) x²−4x+1=0
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\\\x = \dfrac{-(-4) \pm \sqrt{(-4)^2 - 4(1)(1)}}{2(1)}\\\\x = \dfrac{4 \pm \sqrt{16 - 4}}{2}\\\\x = \dfrac{4 \pm \sqrt{12}}{2}[/tex]
x = 2 ± √3
B.) x²−18=0
x² = 18
x = √18
C.) x²+6x+7=0
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\\\x = \dfrac{-(6) \pm \sqrt{(6)^2 - 4(1)(7)}}{2(1)}\\\\x = \dfrac{-6 \pm \sqrt{36 - 28}}{2}\\\\x = \dfrac{-6 \pm \sqrt{8}}{2}[/tex]
x = -3 ± √2
D.) x²−6x+7=0
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\\\x = \dfrac{-(-6) \pm \sqrt{(-6)^2 - 4(1)(7)}}{2(1)}\\\\x = \dfrac{6 \pm \sqrt{36 - 28}}{2}\\\\x = \dfrac{6 \pm \sqrt{8}}{2}[/tex]
x = 3 ± √2
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