Test Index

NCERT Class XI Mathematics - Complex Numbers and Quadratic Equations - Solutions

© examsnet.com
Question : 31 of 52
Marks: +1, -0
x2+x+12x^2+x+\frac{1}{\sqrt{2}} = 0
Solution:  
We have , x2+x+12x^2+x+\frac{1}{\sqrt{2}} = 0
Comparing the given equation with the general form ax2ax^2 + bx + c = 0,
we get a = 1 , b = 1 , c = 12\frac{1}{\sqrt{2}}
∴ x = b±b24ac2a\frac{-b\pm\sqrt{b^2-4ac}}{2a} = 1±(1)24×1×122.1\frac{-1\pm\sqrt{(1)^2-4\times1\times\frac{1}{\sqrt{2}}}}{2.1} = 1±1222\frac{-1\pm\sqrt{1-2\sqrt{2}}}{2}
= 1±(22)1)2\frac{-1\pm\sqrt{-(2\sqrt{2})-1)}}{2} = 1±i2212\frac{-1\pm i\sqrt{2\sqrt{2}-1}}{2}
∴ The roots of the given equation are
1+i2212\frac{-1+i\sqrt{2\sqrt{2}-1}}{2} and 1i2212\frac{-1-i\sqrt{2\sqrt{2}-1}}{2}
© examsnet.com
Go to Question: