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Find the largest natural number a for wh...

Find the largest natural number a for which the maximum value of `f(x)=a-1+2x-x^2` is smaller than the minimum value of `g(x)=x^2-2a x+10-2adot`

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CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
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  2. The roots of the cubic equation (z+ ab)^(3) = a^(3), such that a ne 0...

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  3. Find the largest natural number a for which the maximum value of f(x)=...

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  4. In the Argands plane what is the locus of z(!=1) such that a rg{3/2((2...

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  5. If omega is a complex nth root of unity, then sum(r=1)^n(ar+b)omega^(r...

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  6. Let f(x)=a x^2+b x+c be a quadratic expression having its vertex at (3...

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  7. If |z|=2a n d(z1-z3)/(z2-z3)=(z-2)/(z+2) , then prove that z1, z2, z3...

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  8. If |z1/z2|=1 and arg (z1z2)=0 , then a. z1 = z2 b. |z2|^2 = z1*z2 ...

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  9. Find the least value of n such that (n-2)x^2+8x+n+4>0,AAx in R ,w h ...

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  10. The common roots of the equation Z^3+2Z^2+2Z+1=0 and Z^1985+Z^100+1=0 ...

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  11. If z1 + z2 + z3 + z4 = 0 where bi in R such that the sum of no two ...

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  12. If the inequality (m x^2+3x+4)//(x^2+2x+2)<5 is satisfied for all x i...

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  13. If |(z-2)//(z-3)|=2 represents a circle, then find its radius.

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  14. If z1 is a root of the equation a0z^n+a1z^(n-1)+........+ (a(n-1)) z ...

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  15. If f(x)=(a1x+b1)^2+(a2x+b2)^2+...+(an x+bn)^2 , then prove that (a1b1+...

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  16. If the imaginary part of (2z+1)//(i z+1) is -2, then find the locus of...

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  17. If |2z-1|=|z-2|a n dz1, z2, z3 are complex numbers such that |z1-alph...

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  18. If c is positive and 2a x^2+3b x+5c=0 does not have any real roots, th...

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  19. Find the number of complex numbers which satisfies both the equations ...

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  20. Let omega be the complex number cos((2pi)/3)+isin((2pi)/3). Then the...

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