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Find the condition that one root of the ...

Find the condition that one root of the quadratic equation `ax^(2)+bx+c=0` shall be n times the other, where n is positive integer.

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The correct Answer is:
`nb^(2)=ac(1+n)^(2)`
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VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-QUADRATIC EXPRESSIONS-TEXTUAL EXERCISES
  1. If x^(2)+bx+c=0, x^(2)+cx+b=0 (b ne c) have a common root, then show t...

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  2. Prove that the roots of (x-a)(x-b)=h^(2) are always real.

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  3. Find the condition that one root of the quadratic equation ax^(2)+bx+c...

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  4. Find two consecutive positive even integers, the sum of whose squares ...

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  5. If alpha, beta are the roots of the quadratic equation ax^(2)+bx+c=0, ...

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  6. 2x^(4)+x^(3)-11x^(2)+x+2=0

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  7. Solve 3^(1+x)+3^(1-x)=10

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  8. Solve 4^(x-1)-3.2^(x-1)+2=0

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  9. sqrt((x)/(x-3))+sqrt((x-3)/(x))=(5)/(2)," when "x ne 0and x ne 3

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  10. sqrt((3x)/(x+1))+sqrt((x+1)/(3x))=2," when "x ne 0and x ne -1

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  11. Solve 2(x+(1)/(x))^(2)-7(x+(1)/(x))+5=0," when "x ne 0

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  12. Solve (x^(2)+(1)/(x^(2)))-5(x+(1)/(x))+6=0," when "x ne0

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  13. Find a quadratic equation for which the sum of the roots is 7 and the ...

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  14. If the quadratic equations ax^(2)+2bx+c=0 and ax^(2)+2cx+b=0, (b ne c)...

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  15. If x^(2)-6x+5=0 and x^(2)-3ax+35=0 have common root, then find a.

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  16. If the equation x^(2)+ax+b=0 and x^(2)+cx+d=0 have a common root and t...

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  17. Discuss the signs of the following quadratic expressions when x is rea...

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  18. Discuss the signs of the following quadratic expressions when x is rea...

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  19. For what values of x, the following expressions are negative ? x^(2)...

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  20. For what values of x, the following expressions are negative ? 15+4x...

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