Construct a quadratic equation whose roots ar | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The general form of a quadratic equation is $x^{2} - (	ext{sum of roots})x + (	ext{product of roots}) = 0$.Given roots are $\alpha = \sqrt{2}$ a

Vedclass · Accepted Answer

$x^{2}-3 \sqrt{2} x+4=0$

Vedclass · Answer

(A) The general form of a quadratic equation is $x^{2} - (	ext{sum of roots})x + (	ext{product of roots}) = 0$.Given roots are $\alpha = \sqrt{2}$ and $\beta = 2\sqrt{2}$.Sum of roots $= \alpha + \beta = \sqrt{2} + 2\sqrt{2} = 3\sqrt{2}$.Product of roots $= \alpha \cdot \beta = (\sqrt{2}) \cdot (2\sqrt{2}) = 2 \cdot 2 = 4$.Substituting these values into the general form,we get:$x^{2} - (3\sqrt{2})x + 4 = 0$.

Construct a quadratic equation whose roots are $\sqrt{2}$ and $2 \sqrt{2}$.

Similar Questions

$\sqrt{6+\sqrt{6+\sqrt{6+\cdots}}}$ is equal to

Solve the given two equations and select the correct option.
$I.$ $7x + 4y = 3$
$II.$ $5x + 3y = 3$

Roots of $ax^2 + b = 0$ are real and distinct if

Solve the given two equations and select the correct answer from the given options.
$I. 63x - 94\sqrt{x} + 35 = 0$
$II. 32y - 52\sqrt{y} + 21 = 0$

The length of a rectangular plot is $8 \, m$ greater than its breadth. If the area of the plot is $308 \, m^{2}$,find the length of the plot.

Vedclass Test Series

Exam Paper Generator

Online Exam Module