MCQ
The quadratic equation whose roots are $7 + \sqrt{3}$ and $7 - \sqrt{3}$ is :
- ✓$ x^2-14 x+46=0 $
- B$ x^2-14 x-46=0 $
- C$ x^2+14 x+46=0 $
- D$ x^2+14 x-46=0 $
✓
Answer
Correct option: A.
$ x^2-14 x+46=0 $
Given : $\alpha = 7+\sqrt{3}$ and $\beta= 7-\sqrt{3}$
$\therefore\text{x}^{2}-(\alpha+\beta)\text{ x}+\alpha\beta = {0}$
$\Rightarrow\text{x}^{2} -(7+\sqrt{3}+7-\sqrt{3})\text{ x}+(7+\sqrt{3}) (7-\sqrt{3})=0$
$\Rightarrow\text{x}^{2} - {14}\text{x}+(49-3) = 0$
$\Rightarrow\text{x}^{2} - {14}\text{x}+46 = 0$
$\therefore\text{x}^{2}-(\alpha+\beta)\text{ x}+\alpha\beta = {0}$
$\Rightarrow\text{x}^{2} -(7+\sqrt{3}+7-\sqrt{3})\text{ x}+(7+\sqrt{3}) (7-\sqrt{3})=0$
$\Rightarrow\text{x}^{2} - {14}\text{x}+(49-3) = 0$
$\Rightarrow\text{x}^{2} - {14}\text{x}+46 = 0$
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
The roots of the quadratic equation $9a^2b^2x^2- 16\text{ abcdx} - 25c^2d^2= 0$ are :
→In $\triangle\text{ABC},$ it is given that AB = 9cm, BC = 6cm and CA = 7.5cm. Also, $\triangle\text{DEF}$ is given such that EF = 8cm and $\triangle\text{DEF}\sim\triangle\text{ABC}.$ Then, perimeter of $\triangle\text{DEF}$ 1s:
→If the points A(1, 2), O(0, 0) and C(a, b) are collinear then:
Which of the following cennot be the probability of an event?
In the figure, two equal circles touch each other at T, if QP = 4.5cm, then QR =
Consider the following frequency distribution :
The upper limit of the median class is
→|
Class
|
$0-5$ | $6-11$ | $12-17$ | $18-23$ | $24-29$ |
|
Frequency
|
$13$ | $10$ | $15$ | $8$ | $11$ |
The $5^{\text {th }}$ term of an $A P$ is $20$ and the sum of its $7^{\text {th }}$ and $11^{\text {th }}$ terms is $64 .$ The common difference of the $A.P.$ is.
→If one of the zeros of the cubic polynomial $x^3+ ax^2+ bx + c is -1,$ then the product of the other two zeros is :
→The angle of depression of a car parked on the road from the top of a $150m$ high tower is $30^\circ$ . The distance of the car from the tower $($in metres$)$ is :
→$200$ logs are stacked in such a way that $20$ logs in the bottom row, $19 $logs in the next row, $18$ logs in the row next to it, and so on. The total number of rows is :
→