NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 4: Quadatric Equation - Exercise 4.1Question 8
Class 10 - Mathematics - CHAPTER 4: Quadatric Equation - Exercise 4.1
Question. 8
The quadratic \(2x^2-\sqrt{5}\,x+1=0\) has
(A)
two distinct real roots
(B)
two equal real roots
(C)
no real roots
(D)
more than two real roots
Detailed Answer with Explanation:
We are solving the quadratic equation \(2x^2 - \sqrt{5}x + 1 = 0\).
To check how many real roots it has, we use the discriminant formula:
\(D = b^2 - 4ac\), where \(a=2\), \(b=-\sqrt{5}\), and \(c=1\).
Now, calculate step by step:
\(b^2 = (-\sqrt{5})^2 = 5\).
\(4ac = 4 \times 2 \times 1 = 8\).
So, \(D = 5 - 8 = -3\).
Because \(D < 0\), the quadratic has no real roots. Instead, it will have complex roots.