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Find the greatest value of a non-negative real number `lambda` for which both the equations `2x^2+(lambda-1)x+8=0a n dx^2-8x+lambda+4=0` have real roots.

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CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If x^2+a x+bc=0 a n d x^2+b x+c a=0(a!=b) have a common root, then pro...

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  2. Let alpha,beta are the roots of x^2+b x+1=0. Then find the equation wh...

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  3. Find the greatest value of a non-negative real number lambda for which...

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  4. If a ,b ,c in R such that a+b+c=0a n da!=c , then prove that the root...

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  5. If the fraction (x^3+(a-10)x^2-x+a-6)/(x^3+(a-6)x^2-x+a-10) reduces to...

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  6. If the equation (a-5)x^2+2(a-10)x+a+10=0 has roots of opposite sign, t...

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  7. If alphaa n dbeta are the roots of ax^2+bx+c=0a n dSn=alpha^n+beta^n,...

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  8. If alpha is a root of the equation 4x^2+2x-1=0, then prove that 4alp...

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  9. If both the roots of x^2-a x+a=0 are greater than 2, then find the val...

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  10. If (y^2-5y+3)(x ^2+x+1)<2x for all x in R , then fin the interval i...

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  11. The values of 'a' for which 4^x-(a-4) 2^x+(9a)/4<0 AAx in(1,2) is

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  12. Find the number of positive integral values of k for which kx ^(2) +(k...

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  13. If x^2+2ax+a lt 0 AA x in [1, 2] then find set of all possible values ...

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  14. Given that a ,b ,c are distinct real numbers such that expressions a ...

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  15. Find the number of quadratic equations, which are unchanged by squarin...

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  16. Solve the following: (sqrt(x^2-5x+6)+sqrt(x^2-5x+4))^(x/2)+(sqrt(x^2-...

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  17. Show that the equation A^2//(x-a)+B^2//(x-b)+C^2//(x-c)+...+H^2//(x-h)...

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  18. Find the values of a if x^2-2(a-1)x+(2a+1)=0 has positive roots.

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  19. If alphaa n dbeta,alphaa n dgamma,alphaa n ddelta are the roots of th...

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  20. If alphabeta the roots of the equation x^2-x-1=0 , then the quadratic...

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