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Let lambda,mu be such that the equations...

Let `lambda,mu` be such that the equations `4x^2 - 8x + 3 = 0, x^2 + lambdax - 1 = 0 and 2x^2 + x + mu = 0` may have a common root for each pair of equations but all 3 equations do not have a common root, then `mu xx lambda` equals

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A DAS GUPTA-Equations, Inequation and Expressions-Exercise
  1. If a,b,c, a1,b1,c1 are rational and equations ax^2+2bx+c=0 and a1x^2+2...

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  2. If the equation x^2+ax+12=0 , x^2 +bx +15 =0 and x^2 (a+ b) x+ 36 =0 ...

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  3. Let lambda,mu be such that the equations 4x^2 - 8x + 3 = 0, x^2 + lamb...

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  4. Find the values of a for which x^2-ax+1-2a^2ge0 for real values of x.

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  5. Find the minimum value of 3x^2-6x+7, x in R and also find the correspo...

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  6. Find the maximum value of (2+3x)(1-x),x in R and also find the corresp...

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  7. If f(x) = (x^2 -2x + 4)/(x^2+2x+4), x in R then range of function is

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  8. Range of (x^2-x+1)/(x^2+x+1) is

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

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

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

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

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

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

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

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

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

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

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