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If the sum of the roots of the quadratic...

If the sum of the roots of the quadratic equation `ax^2+bx+c=0` is equal to the sum of the squares of their reciprocals,then prove that `2a^2c=c^2b+b^2a`.

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CHETANA PUBLICATION-Quadratic Equations-EXERCISE
  1. If sum of the roots of quadratic equation is 10 and the product is 9, ...

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  2. Find the values of a,b,c for the following quadratic equation by compa...

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  3. Solve by factorization method: m^2-25=0

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  4. If alpha and beta are roots of quadratic equation, and alpha=-5 and b...

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  5. Vivek is 5 years elder to Kishor. The sum of the reciprocal of their a...

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  6. Solve the following quadratic equation by formula method: x^2+6x+5=0

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  7. If alpha and beta are the roots of quadratic equation x^2+5x-1=0 then,...

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  8. If alpha and beta are the roots of quadratic equation x^2+5x-1=0 then,...

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  9. For doing some work, Pintu takes 6 days more than Nishu. If both work ...

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  10. Find m, if the roots of the quadratic equation (m-12)x^2+2(m-12)x+2=0 ...

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  11. Pratik travels by boat 36 km down a river and back in 8 hours. If the ...

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  12. Two trains leave a railway station at the same time.The first train tr...

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  13. If the sum of the roots of the quadratic equation ax^2+bx+c=0 is equal...

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  14. If the roots of the quadratic equation ax^2+cx+c=0 are in the ratio p:...

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  15. A business man bought some items for ₹600. Keeping 10 items for himsel...

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  16. A man travels by boat 36 km down a river and back in 8 hours. If the s...

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  17. A number consists of two digits whose product is 56.When 9 is subtract...

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  18. Two pipes running together can fill a cinstern in 3 1/13 minutes.If on...

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  19. If the sum of the roots of the quadratic equation is 1/(x+p)+1/(x+q)=1...

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  20. Solve: sqrt(x^2-16)-sqrt(x^2-8x+16)=sqrt(x^2-5x+4).

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