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.
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