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If the equation ax^(2)+2bx+c=0 has real ...

If the equation `ax^(2)+2bx+c=0` has real roots, a,b,c being real numbers and if m and n are real numbers such that `m^(2)gtngt0` then prove that the equation `ax^(2)+2mbx+nc=0` has real roots.

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The correct Answer is:
Hence roots of equation `ax^(2)+2mbx+nc=0` are real
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MOTION-QUADRATIC EQUATION-EXERCISE 4 (PREVIOUS YEAR| JEE MAIN)
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  7. 8. Sachin and Rahul attempted to solve a quadratic equation. Sachin ma...

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  10. If the equation x^(2)+2x+3=0 and ax^(2)+bx+c=0, a,b,c in R have a comm...

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  11. Let alpha and beta be the roots of equation px^2 + qx + r = 0 , p != ...

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  12. If a in R and the equation -3(x-[x])^2+2(x-[x])+a^2=0 (where [x] denot...

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  16. Let a,b,c,p,q be the real numbers. Suppose alpha,beta are the roots of...

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  17. The smallest value of k, for which both the roots of the equation, x^2...

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  18. Q. Let p and q real number such that p!= 0,p^2!=q and p^2!=-q. if alph...

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  20. A value of b for which the equation x^2+b x-1=0,x^2+x+b=0 have one roo...

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  21. Let a in R and let f: R to R be given by f(x) =x^(5) -5x+a. then

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