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If the ratio of the roots of the equatio...

If the ratio of the roots of the equation `x^(2)+px+q=0` is equal to the ratio of the roots of `x^(2)+lx+m=0`, prove that `mp^(2)=ql^(2)`.

A

`p^(2)m = q^(2)l`

B

`pm^(2) = q^(2)l`

C

`p^(2)l = q^(2)m`

D

`p^(2)m = l^(2) q`

Text Solution

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The correct Answer is:
D
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OBJECTIVE RD SHARMA ENGLISH-QUADRATIC EXPRESSIONS AND EQUATIONS -Exercise
  1. If alpha, beta are the roots of the quadratic equation x ^(2)+ px+q=0...

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  2. If the roots of the equation (1)/(x+p) +(1)/(x+q) =1/r are equal in ma...

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  3. If the ratio of the roots of the equation x^(2)+px+q=0 is equal to the...

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  4. Find the value of p for which x+1 is a factor of x^4+(p-3)x^3-(3p-5)x^...

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

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  6. If the equations x^2+p x+q=0 and x^2+p^(prime)x+q^(prime)=0 have a com...

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  7. If the expression x^(2) - 11x + a and x^(2) - 14 x + 2a have a common ...

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  8. If a,b,c are in GP, show that the equations ax^(2)+2bx+c=0 and dx^(2)+...

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  9. Fill in the blanks If the quadratic equations x^2+a x+b=0a n dx^2+b x+...

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  10. Find the values of a for which the roots of the equation x^2+a^2=8x+6a...

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  11. If the sum of the roots of the equation (a+1)x^2=(2a+3)x+(3a+4)=0 is -...

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  12. If one root of the equation (k-1)x^(2) - 10x+ 3 = 0 is the reciproca...

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  13. If b1. b2=2(c1+c2) then at least one of the equation x^2+b1x+c1=0 and ...

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  14. Solve |x^2+4x+3|+2x+5=0.

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  15. For a alt=0, determine all real roots of the equation x^2-2a|x-a|-3...

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  16. If 2+sqrt(3)i is a root of the equation x^2+p x+1=0 , then write the v...

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  17. If tan alpha tan beta are the roots of the equation x^2 + px +q =0(p!...

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  18. Root of the quadratic equation x^2+6x-2=0

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  19. If sum of the roots of ax^(2)+bx+c=0 is equal to the sum of the square...

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  20. For real x , the function (x-a)(x-b)//(x-c) will assume all real value...

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