the number of distinct real roots of x 4 4x 1 0 Simplest way to get the real solutions for x 4 2x 1 0 math stackexchange q 2900199 Rational root test tells us that if there is a rational
The number of distinct real solution of x 4 4 x 3 12 x 2 x 1 0 Q If the equation x 4 4 x 3 2 x 2 12 x a 0 has four distinct real roots then the number of integral values of a is Find the roots of any function by factoring and setting each factor to zero Learn how to solve exponential equations quadratic equations and complex roots with AI explanations and
the number of distinct real roots of x 4 4x 1 0
the number of distinct real roots of x 4 4x 1 0
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Find The Number Of Distinct Real Solutions Of The Equation f f f x 0
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SOLVED The Number Of Distinct Real Roots Of Sin X Cos X Cos X Cos X
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The number of distinct real roots of the equation x 5 x 3 x 2 x 1 x 3x 3 4x 2 2x 4 1 0 is The Fundamental Theorem of Algebra can be used in order to determine how many real roots a given polynomial has Check it out
Now Using Rolles Theorem If f x 0 has n real Roots Then f x 0 has at least n 1 real roots and f x 0 has at least n 2 real roots Or in other words If f x 0 has n roots Then f x 0 has at most n 1 roots If a degree 4 polynomial has 4 real roots then it must have at least 3 local extremes so its derivative must have 3 real roots by repeating this argument its second
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Detailed solution Correct option is B L e t f x x 4 4 x 1 f x 4 x 3 4 f x 0 x 1 x 1 is point of minima f 0 1 f 1 2 f 2 9 f 0 f 1 Learn how to compute and interpret the discriminant of a quadratic polynomial which determines the number and nature of its roots See examples explanations and related topics on completing the square and quadratic formula
To find the number of distinct real roots of the equation x 4 4 x 1 0 we will follow these steps Step 1 Define the function Let f x x 4 4x 1 Step 2 Find the first derivative Amardev Singh Math Square 2 54K subscribers Subscribed 15 397 views 3 months ago JEE Quadratic Equation Past Years The number of distinct real roots of x 4
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the number of distinct real roots of x 4 4x 1 0 - If a degree 4 polynomial has 4 real roots then it must have at least 3 local extremes so its derivative must have 3 real roots by repeating this argument its second