x7+14x5+16x3+30x-560how many real solutions does this equation have

when we differentiate the equation we get0 , \quad \forall x \in \mathbb{R} src=https://files.askiitians.com/cdn1/cms-content/common/latex.codecogs.comgif.latex7x670x448x230gt0_quad_forallx_in_mathbbr.jpg>and hence the function is monotonicand f(0) is negative and then it will continiously increase till infinity and hence will cross the x axis only onceThus it has only one real root

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Algebra> x 7 +14x 5 +16x 3 +30x-560 how man...

x⁷+14x⁵+16x³+30x-560
how many real solutions does this equation have

Manvendra , 9 Years ago

Grade 12

3 Answers

Riddhish Bhalodia

Last Activity: 9 Years ago

when we differentiate the equation we get
$7x^6 + 70x^4 + 48x^2 +30 >0 , \quad \forall x \in \mathbb{R}$
and hence the function is monotonic
and f(0) is negative and then it will continiously increase till infinity and hence will cross the x axis only once
Thus it has only one real root

Prabhakar ch

Last Activity: 9 Years ago

Dear friend this has only one real root all the best for your bright future

SHAIK HAFEEZUL KAREEM

Last Activity: 9 Years ago

and hence the function is monotonicand f(0) is negative and then it will continiously increase till infinity and hence will cross the x axis only onceThus it has only one real root $7x^6 + 70x^4 + 48x^2 +30 >0 , \quad \forall x \in \mathbb{R}$ when we differentiate the equation we get