Find the equation whose roots are 2 x 1-3 and 2 x 2-3- if x 1 and x 2 are the roots of x 2-6 x -7-0A- 2 x-32-62 x-3-7-0B- 2x-32-6-2x-3-7-0C- x-2-32-6x-2-3-7-0D- x-3-22-6x-3-2-7-0

The correct option is D We want to find the equation whose roots are y = 2x + 3, nbsp;if nbsp;x is a root of nbsp;x^2 + 6x + 7 = 0 . y = 2x + 3 nbsp ...

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Byju's Answer

Standard XII

Mathematics

Descartes' Rule

Find the equa...

Question

Find the equation whose roots are $2 x_{1} + 3 a n d 2 x_{2} + 3, i f x_{1} a n d x_{2}$ are the roots of $x^{2} + 6 x + 7 = 0$ .

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Solution

The correct option is D

We want to find the equation whose roots are y = 2x + 3, if x is a root of $x^{2} + 6 x + 7 = 0$ .

y = 2x + 3

2x + 3 = y

$x = \frac{y - 3}{2}$

Replace x by $\frac{y - 3}{2}$ ,

${(\frac{y - 3}{2})}^{2} + 6 (\frac{y - 3}{2}) + 7 = 0 o r {(\frac{x - 3}{2})}^{2} + 6 (\frac{x - 3}{2}) + 7 = 0$

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Similar questions

Q. The quadratic equation whose one root is

(3 + 2 \sqrt{3})

is
(a)

x^{2} + 6 x - 3 = 0

(b)

x^{2} - 6 x - 3 = 0

(c)

x^{2} + 6 x + 3 = 0

(d)

x^{2} - 6 x + 3 = 0

Let f(x) = $x^{2}$ -1, 0 0<x<2 and 2x+3, 2 $\leq$ x<3, The quadratic equation whose roots are ${lim}_{x \to 2^{-}} f (x), a n d {lim}_{x \to 2^{+}} f (x)$