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If the roots of the equation a x^2+2b x+...

If the roots of the equation `a x^2+2b x+c=0` and `b x^2-2sqrt(a c) x+b=0` are simultaneously real, then prove that `b^2=a c`

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RD SHARMA ENGLISH-QUADRATIC EQUATIONS-All Questions
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  4. For what value of k ,(4-k)x^2+(2k+4)x+(8k+1)=0 is a perfect square.

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  5. Prove that the equation x^2(a^2+b^2)+2x(a c+b d)+(c^2+d^2)=0 has no re...

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  6. Find the value of k for which the quadratic equation (k+4)x^2+(k+1)x...

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  7. If the roots of the equation (b-c)x^2+(c-a)x+(a-b)=0 are equal, then ...

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  8. If the roots of the equation (a^2+b^2)x^2-2(a c+b d)x+(c^2+d^2)=0 are ...

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  13. Show that the equation 2(a^2+b^2)x^2+2(a+b)x+1=0 has no real roots, w...

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  14. If the roots of the equation (c^2-a b)x^2-2(a^2-b c)x+b^2-a c=0 are eq...

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  15. If a , b , c , are real number such that a c!=0, then show that at lea...

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  16. Show that the roots of the equation: (x-a) (x -b) +(x- b) (x-c)+ (x- c...

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  18. If the equation (1+m^2)x^2+2m c x+(c^2-a^2)=0 has equal roots, prove t...

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  19. If -5 is a root of the quadratic equation 2x^2+p x-15=0 and the quadra...

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  20. Find the values of p for whch the equadratic equation (2p+1)x^2-(7p+2...

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