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If the quadratic polynomials defined on ...

If the quadratic polynomials defined on real coefficient
`P(x)=a_(1)x^(2)+2b_(1)x+c_(1)` and `Q(x)=a_(2)x^(2)+2b_(2)x+c_(2)` take positive values `AA x in R`, what can we say for the trinomial `g(x)=a_(1)a_(2)x^(2)+b_(1)b_(2)x+c_(1)c_(2)` ?

A

`f (x) lt 0 AA x in R`

B

`f (x) gt 0 AA x in R`

C

`f (x)` takes both positive and negativce values

D

Nothing can be said about `f (x)`

Text Solution

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The correct Answer is:
B
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VK JAISWAL-QUADRATIC EQUATIONS -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
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  12. The number of negative intergral values of m for which the expression ...

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  15. If x ^(2) -3x+2 is a factor of x ^(4) -px ^(2) +q=0, then p+q=

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  16. The expression x^2 + 2xy + ky^2 + 2x + k = 0 can be resolved into two ...

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  17. The curvey y = (a +1) x ^(2) + 2 meets the curve y = ax +3, a ne -1 in...

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  18. Find the number of integral vaues of 'a' for which the range of functi...

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  19. When x ^(100) is divided by x ^(2) -3x +2, the remainder is (2 ^(k +1)...

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  20. Let p (x) be a polynomial equation of least possible degree, with rati...

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  21. The range of values k for which the equation 2 cos ^(4)x-sin ^(4)x +k=...

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