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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Grade 12Algebra

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

Manvendra

10 Years agoGrade 12

3 Answers

Riddhish Bhalodia

10 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

10 Years ago

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

SHAIK HAFEEZUL KAREEM

10 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