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Given that a ,b ,c are distinct real num...

Given that `a ,b ,c` are distinct real numbers such that expressions `a x^2+b x+c ,b x^2+c x+a and,c x^2+a x+b` are always non-negative. Prove that the quantity `(a^2+b^2+c^2)/(a b+b c+c a)` can never lie in `(-oo,1)` `uu` `[4 , oo)` .

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CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
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  3. Given that a ,b ,c are distinct real numbers such that expressions a x...

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

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

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

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

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

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  10. If a(p+q)^2+2b p q+c=0 and a(p+r)^2+2b p r+c=0 (a!=0) , then which one...

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  11. If alpha1,alpha2 are the roots of equation x ^2-p x+1=0a n dbeta1,bet...

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  12. Suppose A, B, C are defined as A=a^2b+a b^2-a^2c-a c^2 , B=b^2c+b c^2-...

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  13. The integral value of m for which the root of the equation m x^2+(2m-1...

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  14. If b1. b2=2(c1+c2) then at least one of the equation x^2+b1x+c1=0 and ...

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  15. If the root of the equation (a-1)(x^2-x+1)^2=(a+1)(x^4+x^2+1) are real...

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  16. If alpha and beta are roots of the equation a x^2+b x+c=0, then the ro...

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  17. If a ,b ,c ,d in R , then the equation (x^2+a x-3b)(x^2-c x+b)(x^2-dx...

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  18. Graph of y = f(x) is as shown in the following figure. Find th...

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  19. In how many points graph of y=x^3-3x^2+5x-3 intersect the x-axis?

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  20. The quadratic polynomial p(x) has the following properties:p(x)geq0 fo...

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