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Quadratic Equations in One Variable — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsQuadratic Equations in One Variable1 Mark
MCQ
The quadratic equation $2 x^2-\sqrt{5} x+1=0$ has
  • A
    two distinct real roots
  • B
    two equal real roots
  • ✓
    no real roots
  • D
    more than two real roots
✓

Answer

Correct option: C.
no real roots
$C$
The quadratic equation $2 x^2-\sqrt{ 5} x+1=0$ has no real roots.
Explanation:
Given equation is $2 x^2-\sqrt{5} x+1=0$
On comapring with $ax^2 + bx + c = 0$, we get
$a=2, b=-\sqrt{5}$ and $c=1$
$\therefore$ Discriminant, $D = b^2 – 4ac$
$=(-\sqrt{5})^2-4 \times(2) \times(1)$
$ =5-8 $
$ =-3<0$
Since, discrimant is negative,
Therefore quadratic equation$2 x^2-\sqrt{5} x+1=0$has no real roots
i.e., imaginary roots.

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