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Show that the roots of the equation x^2 ...

Show that the roots of the equation `x^2 + px - q^2 = 0` are real for all real values of p and q.

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`D=(p^(2)+4q^(2))ge0.`
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RS AGGARWAL-QUADRATIC EQUATIONS -Exercise 4D
  1. Find the nature of the roots of the following quadratic equations: (...

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  2. Show that the equation 2(a^2+b^2)x^2+2(a+b)x+1=0 has no real roots whe...

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  3. Show that the roots of the equation x^2 + px - q^2 = 0 are real for al...

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  4. For what values of k are the roots of the quadratic equation 3x^(2)+2k...

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  5. For what value of k are the roots of the quadratic equation kx(x-2sqrt...

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  6. Find the value of p for which the quadratic equation 4x^2+px+3=0 has e...

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  7. Find the nonzero value of k for which the roots of the quadratic equat...

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  8. (i) Find the values of k for which the quadratic equation (3k+1)x^(2)+...

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  9. Find the values of p for whch the equadratic equation (2p+1)x^2-(7p+2)...

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  10. Find the value of p for which the quadratic equation (p+1)x^2+ -6(p+1)...

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  11. If -5 is a root of the quadratic equation 2x^2+p x-15=0 and the quadra...

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  12. If 3 is a root of the quadratic equation x^(2)-x+k=0 find the value of...

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  13. If -4 is a root of the equation x^2+2x+4p=0 then find the value of k f...

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  14. If the equation (1+m^2)x^2+2m c x+(c^2-a^2)=0 has equal roots, prove t...

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  15. If the roots of the equation (c^2-a b)x^2-2(a^2-b c)x+b^2-a c=0 are eq...

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  16. Find the values of p fro which the qadratic equation 2x^(2)+px+8=0 has...

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  17. Find the value of alpha for which the equation (alpha-12)x^(2)+2(alpha...

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  18. For what real values of k the equation 9x^2 +8 Kx +16=0 have real and ...

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  19. Find the values of k for which the given quadratic equation has real a...

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  20. If a and b are real and aneb then show that the roots of the equation ...

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