Question

Find the roots of quadratic equation 9x²-15x+6 by completing square method​

Answer 1

Answer:

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Given Equation is 9x^2 - 15x + 6 = 0.

(i) Divide throughout by 9.

⇒ x^2 - (15/9) x + (6/9) = 0

⇒ x^2 - (5/3) x + (2/3) = 0

(ii) Rewrite the equation with the constant term on the right side.

⇒ x^2 - (5/3) x = -2/3

(iii) Complete the square by adding the square of one-half of coefficient.

⇒ x^2 - (5/3)x + (5/6)^2 = -2/3 + (5/6)^2

⇒ x^2 - (5/3) x + (5/6)^2 = 1/36

(iv) Write the left side as square.

⇒ (x - 5/6)^2 = 1/36

⇒ x - 5/6 = √1/36

⇒ x - 5/6 = 1/6

(v) Equate and solve.

(a)

⇒ x - 5/6 = 1/6

⇒ x = 1/6 + 5/6

⇒ x = 1.

(b)

⇒ x - 5/6 = -1/6

⇒ x = -1/6 + 5/6

⇒ x = 2/3.

Therefore, roots are 1 and 2/3.

Answer 2

Answer:

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