Question

x²-6x + 9=0 by quadratic formula​

Answer 1

Answer :

• x = 3

Given :

• x² - 6x + 9 = 0

To find :

• Roots of the equation

Solution :

》x² - 6x + 9 = 0

by using the quadratic formula

Compare ax² + bx + c

》x =  -b ± √b²- 4ac / 2a

Where ,

• a = 1
• b = - 6
• c = 9

》x =  -b ± √b²- 4ac / 2a

》x =  -6 ± √(-6)²- 4(1)(9) / 2(1)

》x =  -6 ± √36 - 36  / 2

》x = 3 ± 0

》x = 3

or

》x² - 6x + 9 = 0

》x² - 3x - 3x + 9 = 0

》x(x - 3) - 3(x - 3) = 0

》(x - 3)² = 0

》x - 3 = 0 or x = 3

Hence, x² - 6x + 9 = 0 is x = 3

Answer 2

Given Equation:-

• x² - 6x + 9 = 0

To Find:-

• It's Roots

Formula used:-

• Quadratic Formula ${\boxed{x=\dfrac{-b±\sqrt{b^2-4ac}}{2a}}}$

Solution:-

Comparing the given equation with standard equation i.e. ax² + bx + c = 0. We get,

• a = 1

• b = -6

• c = 9

Putting the values in the Formula,

$\implies\:x=\dfrac{-b±\sqrt{b^2-4ac}}{2a}$

$\implies\:x=\dfrac{-(-6)±\sqrt{(-6)^2-4(1)(9)}}{2(1)}$

$\implies\:x=\dfrac{-6±\sqrt{36-36}}{2}$

$\implies\:x=\dfrac{-6±\sqrt{0}}{2}$

$\implies\:x=\dfrac{-6}{2}$

${\boxed{\implies\:x=-3}}$

Hence, The root of the given equation is -3.

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