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Find the roots of the following quadratic equations, if they exist, by the method of completing the square: 2x^2 – 7x +3 = 0

Find the roots of the following quadratic equations, if they exist, by the method of completing the square:
2x^2 – 7x +3 = 0

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5963 Points
9 months ago
Dear student

⇒2x^2–7x=-3
Dividing by 2 on both sides, we get⇒x^2-7x/2 = -3/2
⇒x^2-2 × x ×7/4 = -3/2

On adding (7/4)^2to both sides of equation, we get

⇒(x)^2-2×x×7/4 +(7/4)^2= (7/4)^2-3/2
⇒(x-7/4)^2= (49/16)–(3/2)
⇒(x-7/4)^2= 25/16
⇒(x-7/4)^2= ±(5/4)^2

⇒x= 7/4 ± 5/4
⇒x= 7/4 + 5/4 or x = 7/4–5/4
⇒x = 12/4 or x = 2/4
⇒x = 3 or x = ½

Thanks

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