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Chapter 8: Quadratic Equations Exercise – 8.4 Question: 1 By using the method of completing the square, find the roots of quadratic equations. Solution: So, the roots for the given equation are: x = 3√2or x = √2. Question: 2 By using the method of completing the square, find the roots of quadratic equations. 2x2 − 7x + 3 = 0 Solution: 2x2 - 7x + 3 = 0 x = 12/4 or x = 2/4 x = 3 or x = ½ Question: 3 By using the method of completing the square, find the roots of quadratic equations. 3x2 + 11x + 10 = 0 Solution: 3x2+ 11x + 10 = 0 x = (-5)/3 or x = - 2 Question: 4 By using the method of completing the square, find the roots of quadratic equations. 2x2 + x − 4 = 0 Solution: 2x2 + x − 4 = 0 Are the two roots of the given equation. Question: 5 By using the method of completing the square, find the roots of quadratic equations. 2x2 + x + 4 = 0 Solution: 2x2 + x + 4 = 0 x2 + x2 + 2 = 0 Since, √(-31) is not a real number, Therefore, the equation doesn’t have real roots. Question: 6 By using the method of completing the square, find the roots of quadratic equations. Solution: Therefore, x = (- √3)/2 and x = (- √3)/2. Are the real roots of the given equation. Question: 7 By using the method of completing the square, find the roots of quadratic equations. Solution: Question: 8 By using the method of completing the square, find the roots of quadratic equations. Solution: Question: 9 By using the method of completing the square, find the roots of quadratic equations. Solution: x = √2 or x = 1. Question: 10 By using the method of completing the square, find the roots of quadratic equations. x2 - 4ax + 4a2 - b2 = 0 Solution: x2 - 4ax + 4a2 - b2 = 0 x2 - 2(2a).x + (2a)2 - b2 = 0 (x - 2a)2 = b2 x - 2a = ± b x - 2a = b or x - 2a = - b x = 2a + b or x = 2a - b Therefore, x = 2a + b or x = 2a - b are the two roots of the given equation.
By using the method of completing the square, find the roots of quadratic equations.
So, the roots for the given equation are: x = 3√2or x = √2.
2x2 − 7x + 3 = 0
2x2 - 7x + 3 = 0
x = 12/4 or x = 2/4
x = 3 or x = ½
3x2 + 11x + 10 = 0
3x2+ 11x + 10 = 0
x = (-5)/3 or x = - 2
2x2 + x − 4 = 0
Are the two roots of the given equation.
2x2 + x + 4 = 0
x2 + x2 + 2 = 0
Since, √(-31) is not a real number, Therefore, the equation doesn’t have real roots.
Therefore, x = (- √3)/2 and x = (- √3)/2. Are the real roots of the given equation.
x = √2 or x = 1.
x2 - 4ax + 4a2 - b2 = 0
x2 - 2(2a).x + (2a)2 - b2 = 0
(x - 2a)2 = b2 x - 2a = ± b x - 2a = b or x - 2a
= - b x = 2a + b or x = 2a - b
Therefore, x = 2a + b or x = 2a - b are the two roots of the given equation.
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Chapter 8: Quadratic Equations Exercise –...
