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If the sum of the roots of the equation `x^2-px+q=0` be three times their difference show that, `2p^2=9q`.

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CHHAYA PUBLICATION-QUADRATIC EQUATIONS-EXERCISE 5A(Short answer type question)
  1. If p and q are the roots of the equation 3x^2+6x+2=0, show that the eq...

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  2. If the sum of the roots of a quadratic equation is 2 and the sum of th...

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  3. If the sum of the roots of the equation x^2-px+q=0 be three times thei...

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  4. If the roots of the equation ax^2+bx+c=0 are in the ratio 3:4 show tha...

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  5. If one root of the equation x^2+(5a+2)x+5a+2=0 is five times the other...

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  6. Find the quadratic equation whose roots are the cubes of the roots of ...

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  7. The ratio of the roots of the equation ax^2+bx+c=0is r:1 Prove that, b...

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  8. If the roots of the equation px^2+rx+r=0 are in the ratio a:b, prove t...

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  9. In a quadratic equation of the form x^2+mx+n=0 the constant term is mi...

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  10. For what value of m the roots of the equation (m+1)x^2+2(m+3)x+m+8=0 a...

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  11. If one root of the equation x^2+bx+8=0 be 4 and the roots of the equat...

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  12. For what value of m the roots of the equation 3/(x+3+m)+5/(x+5+m)=1 ar...

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  13. Find the condition so that the roots of the equation a/(x-a)+b/(x-b)=5...

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  14. Show that the roots of each of the following equations are rational(a,...

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  15. Show that the roots of each of the following equations are rational(a,...

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  16. Show that the roots of the equation (a^2-bc)x^2+2(b^2-ca)x+c^2-ab=0 ar...

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  17. If one root of the equation qx^2+px+q=0 (p,q are real) be imaginary, s...

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  18. If the roots of the equation qx^2+2px+2q=0 are real and unequal, prove...

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  19. If the roots of the equation x^2-2(a+b)x+a(a+2b+c)=0 be equal , prove ...

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  20. If the equation x^2+px+q=0andx^2+p'x+q'=0 have a common root , prove t...

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