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​ x 7 +14x ​ ​5 +16x 3 +30​x-560 ​how many real solutions does this equation have

x7+14x​5+16x3+30​x-560
​how many real solutions does this equation have

Grade:12

3 Answers

Riddhish Bhalodia
askIITians Faculty 434 Points
5 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
577 Points
5 years ago
Dear friend this has only one real root all the best for your bright future
SHAIK HAFEEZUL KAREEM
109 Points
5 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 root7x^6 + 70x^4 + 48x^2 +30 >0 , \quad \forall x \in \mathbb{R}when we differentiate the equation we get

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