The number of solutions of y - x 2-10 x -22 and y - e x isA- 0B- 1C- 2D- 3

The correct option is C 2Given curve is nbsp;y = x^2+10x+22 ⇒ y = (x+5)^2 3 Curve of y=x^2 is Now, shift this curve towards left by 5 units ⇒ y = (x+5 )^ ...

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Standard XII

Mathematics

f(x) Transforms to f(-x)

The number of...

Question

The number of solution(s) of $y = x^{2} + 10 x + 22$ and $y = e^{x}$ is

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Solution

The correct option is C $2$
Given curve is $y = x^{2} + 10 x + 22$
$\Rightarrow y = (x + 5)^{2} - 3$

Curve of $y = x^{2}$ is

Now, shift this curve towards left by $5$ units
$\Rightarrow y = {(x + 5)}^{2}$

Now move this curve downwards by $3$ units
$\Rightarrow y = {(x + 5)}^{2} - 3$ and drawing $y = e^{x}$ , we get

As $y = x^{2} + 10 x + 22$ and $y = e^{x}$ intersects at two distinct points, so the number of solutions is $2.$

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The number of solution(s) of y=x2+10x+22 and y=ex is

The number of solution(s) of $y = x^{2} + 10 x + 22$ and $y = e^{x}$ is