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If `a_0, a_1, a_2, a_3` are all the positive, then `4a_0x^3+3a_1x^2+2a_2x+a_3=0` has least one root in `(-1,0)` if (a) `a_0+a_2=a_1+a_3 ` and `4a_0+2a_2>3a_1+a_3` (b) `4a_0+2a_2<3a_1+a_3` (c) `4a_0+2a_2=3a_1+a_0`and `4a_0+a_2lta_1+a_3` (d) none of these

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CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If |z-(1/z)|=1, then a. (|z|)(m a x)=(1+sqrt(5))/2 b. (|z|)(m in)=(s...

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  2. zo is one of the roots of the equation z^n cos theta0+ z^(n-1) cos th...

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  3. If a0, a1, a2, a3 are all the positive, then 4a0x^3+3a1x^2+2a2x+a3=0 ...

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  4. If 1,z1,z2,z3,.......,z(n-1) be the n, nth roots of unity and omega b...

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  5. If a x ^2+b x+c=0 has imaginary roots and a-b+c >0 then the set of poi...

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  6. All the values of ' a ' for which the quadratic expression a x^2+(a-2)...

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  7. If the equation z^3 + (3 + i)(z^2) - 3z - (m + i)= 0, m in R , has at ...

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  8. If a+b+c=0,a^2+b^2+c^2=4,t h e na^4+b^4+c^4 is.

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  9. Let P(x) and Q(x) be two polynomials. If f(x) = P(x^4) + xQ(x^4) is di...

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  10. Find the solution set of the system x+2y+z=1 2x-3y-w=2 xgeq0,ygeq0,zge...

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  11. If amp(z1z2)=0 and absz1=absz2=1, then

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  12. mn squares of equal size are arranged to form a rectangle of dimension...

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  13. Prove that ln(1+x) < x for x > 0.

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  14. Form a quadratic equation whose roots are -4 and 6.

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  15. If |(z-z1)/(z-z2)|=3,w h e r ez1a n dz2 are fixed complex numbers and ...

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  16. If a,b,c are odd integere then about that ax^2+bx+c=0, does not have r...

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  17. if arg(z+a)=pi/6 and arg(z-a)=(2pi)/3 then

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  18. Values (s)(-i)^(1/3) is/are (sqrt(3)-i)/2 b. (sqrt(3)+i)/2 c. (-sqrt(...

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  19. if costheta , sinphi , sintheta are in g.p then check the nature of ro...

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  20. Given z=(1+isqrt(3))^(100), then [Re(z)//Im(z)] equals (a)2^(100) ...

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