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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)=ca(1+n)^(2)`
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AAKASH SERIES-QUADRATIC EQUATIONS & EXPRESSIONS-PRACTICE EXERCISE
  1. Find the condition that one root of the quadratic equation ax^(2)+bx+c...

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  2. If (3x+2)/(2x+3)=(4x+3)/(3x+4), then x =

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  3. The roots of the equation (b-c) x^2 +(c-a)x+(a-b)=0are

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  4. A root of the equation (x-2)(x-3)=(155 xx 78)/((77)^(2))

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  5. A root of the equation (a+c)/(x+a)+(b+c)/(x+b)=(2(a+b+c))/(x+a+b) i...

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  6. If (x-a+2b)^(2)+(x-2a+b)^(2)=(a+b)^(2), then one value of x is

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  7. If alpha, beta are the rootsof 6x^(2)-4sqrt2 x-3=0, then alpha^(2)beta...

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  8. Assertion (A): If alpha, beta are the roots of x^(2)-x+1=0, then alpha...

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  9. If alpha , beta are the roots of ax ^2 + bx +c=0 then alpha ...

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  10. If w, w^(2) are the roots of x^(2)+x+1=0 and alpha, beta are the roots...

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  11. If the roots ax^(2)+bx+c=0 are (3)/(2),(4)/(3) then (a+b+c)^(2) =

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  12. If a, b are the roots of x^(2)+x+1=0, then a^(2)+b^(2) is

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  13. If alpha, beta are the roots of x^(2)+x+1=0, then alpha^(-2)+beta^(-2)...

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  14. If alpha, beta are the roots of ax^(2)+bx+c=0, alpha beta=3 and a, b, ...

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  15. If alpha, beta are the roots of x^(2)+ax+12=0 such that alpha-beta=1, ...

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  16. The values of P for which the difference between the roots of the equa...

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  17. IF the different between the roots of x^(2) -px+q=0 is 2, then ...

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  18. If x-2 is a factor of x^(2)+6x+16b, then b =

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  19. If the sum of the roots of kx^(2) + 2x + 3k = 0 is equal to their prod...

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  20. If the sum of the roots of x^(2) + bx + 1 = 0, is equal to the sum of ...

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  21. IF alpha , beta are the roots of ax^2 + bx +c=0 then the equat...

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