The number of real solutions of x7+5 x3+3 x+1= 0 is equal to.

Question

The number of real solutions of x7+5 x3+3 x+1= 0 is equal to. (A) 0 (B) 1 (C) 3 (D) 5

Tardigrade Admin · Accepted Answer

f(x)=x7+5 x3+3 x+1 f prime(x)=7 x6+15 x2+3 > 0 ∴ f ( x ) is strictly increasing function <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/475b866e752a2af97c6b108ba2006079-.png" /> ∴ no. of real solution = 1

Q. The number of real solutions of $x^{7} + 5 x^{3} + 3 x + 1 = 0$ is equal to_____.

0

1

3

5

$f (x) = x^{7} + 5 x^{3} + 3 x + 1$
$f^{'} (x) = 7 x^{6} + 15 x^{2} + 3 > 0$
$∴ f (x)$ is strictly increasing function

$∴$ no. of real solution $= 1$

Q. The number of real solutions of x7+5x3+3x+1=0 is equal to_____.

0

1

3

5

f(x)=x7+5x3+3x+1 f′(x)=7x6+15x2+3>0 ∴f(x) is strictly increasing function ∴ no. of real solution =1

Q. The number of real solutions of $x^{7} + 5 x^{3} + 3 x + 1 = 0$ is equal to_____.

$f (x) = x^{7} + 5 x^{3} + 3 x + 1$
$f^{'} (x) = 7 x^{6} + 15 x^{2} + 3 > 0$
$∴ f (x)$ is strictly increasing function

$∴$ no. of real solution $= 1$