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If x is real, show that the expression (...

If x is real, show that the expression `(4x^2+36 x+9)/(12 x^2+8x+1)` can have any real value .

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A DAS GUPTA-Equations, Inequation and Expressions-Exercise
  1. Range of (x^2-x+1)/(x^2+x+1) is

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  2. If for all real x (x+a)/(x^2+b x+c^2) cannot lie between two limits, ...

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  3. If x is real, show that the expression (4x^2+36 x+9)/(12 x^2+8x+1) can...

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  4. If x in R ,a n da ,b ,c are in ascending or descending order of magni...

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  5. If f(x)=(ax^2+x-2)/(a+x-2x^2) has the range R when x in R then

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  6. Let f(x)=(mx^2+3x+4)/(x^(2)+3x+4) , m in R . If f(x) lt 5 for all x i...

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  7. For x in R, the expression (x^2+2x+c)/(x^2+4x+3c) can take all real va...

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  8. x^2-x y+y^2-4x-4y+16=0 represents a. a point b. a circle c. a pair...

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  9. If the expression x^2+2(a+b+c)x+3(bc+ca+ab) is a perfect square then

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  10. If (a1x^2 +bx+c1)y+(a2x^2+b2x+c1)=0 find condition that x is a ration...

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  11. 52 Show that a(b - c)x^2 + b(c - a)xy + c(a - b)y^2 will be a perfect...

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  12. For what value of k, (x + y + z)^2 + k(x^2 +y^2 + z^2) can be resolve...

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  13. If (x-1)^(2) is a factor of ax^(3) +bx^(2) +c then roots of the equa...

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  14. If a1x^3 + b1x² + c1x + d1 = 0 and a2x^3 + b2x^2+ c2x + d2 = 0 have a ...

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  15. If |x|+|x-1|=3 then x= .

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  16. The solution-set of the equation log5log2(sqrt(4x+2)+2sqrt2)=0 is .

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  17. Fill in the blanks If x<0,y<0,x+y+(x//y)=(1//2)a n d(x+y)(x//y)=-(1//2...

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  18. The number of real solutions of the equation |x^2|-3|x|+2=0 is .

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  19. If x-=2+^(2//3)"then the value"(x^(3)-6x^(2)+6x)is

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  20. The AM of the roots of x^2-12x+3=0 is .

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