MCQ
If the equation $x^2- ax + 1 = 0$ has two distinct roots, then :
- A$|a| = 2$
- B$|a| < 2$
- ✓$|a| >2$
- DNone of these.
✓
Answer
Correct option: C.
$|a| >2$
The given quadric equation is $x^2-a x+1=0$, and roots are dostinct.
Then fond the value of a.
Here $, a = 1, b = a$ and $c = 1$
As we know that $D = D=b^2-4 a c$
Putting the value of $a = 1, b = a$ and $c = 1$
$ =(a)^2-4 \times 1 \times 1 $
$ =a^2-4$
The given equation will have real and distinct roots, if $D > 0$
$ a^2-4>0 $
$ a^2>4$
$\text{a}>\sqrt{4}$
$\text{a}>\pm2$
Therefore, the value of $|a| > 2$
Thus, the correct answer is $(c)$
Then fond the value of a.
Here $, a = 1, b = a$ and $c = 1$
As we know that $D = D=b^2-4 a c$
Putting the value of $a = 1, b = a$ and $c = 1$
$ =(a)^2-4 \times 1 \times 1 $
$ =a^2-4$
The given equation will have real and distinct roots, if $D > 0$
$ a^2-4>0 $
$ a^2>4$
$\text{a}>\sqrt{4}$
$\text{a}>\pm2$
Therefore, the value of $|a| > 2$
Thus, the correct answer is $(c)$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
A metallic cylinder of radius $8 \ cm$ height $2 \ cm$ is melted and converted into a right circular cone of height $6 \ cm .$ The radius of the base of this cone is
→If $\sin A +\sin ^2 A=1$, then $\cos ^2 A+\cos ^4 A= ?$
→In the given figure, three circles with centres $A, B, C$ respectively touch each other externally. If $A B=5 cm , B C=7 cm$ and $C A=6 cm$, then the radius of the circle with centre $A$ is
→If the area of a sector of a circle bounded by an arc of length $5\pi\text{cm}$ is equal to $20\pi\text{cm}^2,$ then its radius is:
→If $\theta=30^{\circ}$ then the value of $3 \tan \theta$ is
→Directions : In the following questions, the Assertions $(A)$ and Reason $(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following :
Assertion : The graphical representation of a pair of equations $4x + 3y - 1 = 5$ and $12x + 9y = 15$ will be parallel lines.
Reason : if the the given pair of equations has no solution.That means, the lines representing the given pair of equations are parallel to each other.
→Assertion : The graphical representation of a pair of equations $4x + 3y - 1 = 5$ and $12x + 9y = 15$ will be parallel lines.
Reason : if the the given pair of equations has no solution.That means, the lines representing the given pair of equations are parallel to each other.
Which of the following cannot be the probability of occurrence of an event?
$\frac{\tan\theta}{\sec\theta-1}+\frac{\tan\theta}{\sec\theta + 1}$ is equal to :
→The smallest number by which $\sqrt{27}$ should be multiplied so as to get a rational number is
→A card is drawn at random from a pack of $52$ cards. The probability that the card is drawn is neither an ace nor a king is :
→