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Let 'p' & 'q' be real numbers . Prove th...

Let 'p' & 'q' be real numbers . Prove that the cubic `y = x^(3) + p x + q` has three distinct real roots, if `4 p^(3) + 27 q^(2) lt 0 `.

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MOTION-MAXIMA AND MINIMA -EXERCISE - 4 (LEVEL - II)
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  3. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

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  4. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

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  5. Consider the function f : (-oo , oo) to (-oo , oo) defined by f(x) = (...

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  6. Let p(x) be a polynomial of degree 4 having extremum at x = 1, 2 and u...

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  8. Let f,g and h be real-valued functions defined on the interval [0,1] b...

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  9. Let f be a function defined on R (the set of all real numbers) such th...

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  10. The number of distinct real roots of x^(4)-4x^(3)+12x^(2)+x-1=0

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  11. Let p(x) be a real polynomial of least degree which has a local maximu...

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  12. Let I RvecI R be defined as f(x)=|x|++x^2-1|dot The total number of po...

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  13. If f(x) = underset(0)overset(x)inte^(t^(2)) (t-2) (t-3) dt for all x ...

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  14. A rectangular sheet of fixed perimeter with sides having their lengths...

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