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If a, b, c, d are real numbers such that `(a+2c)/(b+3d)+(4)/(3)=0`. Prove that the equation `ax^(3)+bx^(2)+cx+d=0` has atleast one real root in (0, 1).

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FIITJEE-QUADRATIC EQUATION & EXPRESSION -ASSIGNMENT PROBLEMS (SUBJECTIVE) Level - II
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  2. Let 4x^(2)-4(alpha-2)x + alpha-2=0(alpha in R) be a quadratic equation...

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  3. Let 4x^(2)-4(alpha-2)x + alpha-2=0(alpha in R) be a quadratic equation...

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  4. Let 4x^(2)-4(alpha-2)x + alpha-2=0(alpha in R) be a quadratic equation...

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  5. Let 4x^(2)-4(alpha-2)x + alpha-2=0(alpha in R) be a quadratic equation...

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  6. Let 4x^(2)-4(alpha-2)x + alpha-2=0(alpha in R) be a quadratic equation...

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  7. Let 4x^(2)-4(alpha-2)x + alpha-2=0(alpha in R) be a quadratic equation...

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  8. For what real values of a do the roots of the equation x^2-2x-(a^2-1)=...

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  9. If a1, a2, a3 ......an (n>= 2) are read and (n-1) a1^2 -2na2 < 0 then...

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  11. Find all the values of p for which the equation x^(4)-4x^(3)-8x^(2)+p=...

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  12. Find all the values of p for which the equation x^(4)-4x^(3)-8x^(2)+p=...

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  14. If a, b, c, d are real numbers such that (a+2c)/(b+3d)+(4)/(3)=0. Prov...

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  15. If f(x) is a real valued polynomial and f (x) = 0 has real and distinc...

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  16. Let a ,b in na n a > 1. Also p is a prime number. If a x^2+b x+c=p fo...

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  17. If 2x^(3)+ax^(2)+bx+4=0 (a, b are positive real numbers) has 3 real ro...

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  18. Prove that x^(4)+2x^(2)-x+2=0 has no real solution.

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  19. The value of the positve integer n for which the quadratic equation su...

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  20. Find the value of a such that -a.9^(x)+(a-2)3^(x)-((5)/(4)a-1)gt 0 for...

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