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The equation ax^2+2x+a=0 has two distinc...

The equation `ax^2+2x+a=0` has two distinct roots,if

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If 2 is a root of the equation x^2+px-8 = 0 and the equation x^2 + px + q = 0 has equal roots, find p, q .

If -3 is a root of the equation x^2+ px + 6 = 0 and the equation x^2 +px +q = 0 has equal roots, find p,q .

If one root of the equation x^2+ax+3=0 is 1,then its other root is a)2 b)-2 c)3 d)-3

If - 4 is a root of x^2 + px -4 = 0 and the equation x^2 + px + q = 0 has equal roots find p and q.

If one root of the equation x^2 +px+ 12 = 0 be 4 and if the roots of the equation x^2 + px + q = 0 be equal, find q

For what of k the equation 2x^2-2kx+k=0 will have Two unequal roots. Further if k is a rational number, for what value or values, of k, the roots will be rational.

If the roots of the equation ax^2 + bx + c = 0 are in the ratio 2:3 , then prove that 6b^2 = 25ac

If one root of the equation ax^2+ bx+ c=0 be n times the other,show that (n+1)^2/n=b^2/(ac)

If one root of the equation x^2 - px + q = 0 be twice the other, show that 2p^2 = 9q

If alpha , beta be the roots of the equation ax^2 + bx + c = 0 , form the quadratic equation whose roots are 1/alpha , 1/beta

R G PUBLICATION-QUADRATIC EQUATIONS-EXERCISE
  1. The quadratic equation is a)x(x+1)+8=(x+2)(x-2) b)x^2+1/x^2=5 c)x^2...

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  2. The roots of the quadratic equation x^2+6x+5=0 a)5,-1 b)2,3 c)6,-1 ...

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  3. If ax^2+bx+c=0has equal roots,then,c= a)b/(2a) b)-b/(2a) c)b^2/(4a) d...

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  4. If x^2-4x+p=0has real roots then

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  5. The roots of the equation x^2-sqrt3x-x+sqrt3=0 are

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  6. The roots of the equation ax^2+x+b=0 are equal if

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  7. If x=1 is a common root of equations ax^2+ax+3=0 and x^2+x+b=0then ab=

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  8. The equation ax^2+2x+a=0 has two distinct roots,if

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  9. If x^2+2(k+2)x+9k=0 has equal roots then k= a)-1,4 b)1,-4 c)-1,-4 ...

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  10. If 8 is a root of the equation x^2-10x+k=0then the value of k is a)1...

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  11. If a and b are the roots of the equation x^2+ax+b=0,then a+b=

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  12. If one root of the equation x^2+ax+3=0 is 1,then its other root is ...

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  13. The positive value of k for which the equation x^2+kx+64=0 and x^2-8x+...

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  14. The roots of the equation sqrt2x^2+5x+2sqrt2=0 are a)Rational b)Irr...

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  15. The value Of sqrt(6+sqrt(6+sqrt(6+.....))) is a)-2 b)3.5 c)3 d)4

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  16. For the quadratic equation x^2-2x+1=0 the value of x+1/x is a)1 b)-...

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  17. If the equation (a^2+b^2)x^2-2(ac+bd)x+(c^2+d^2)=0 has equal roots, th...

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  18. If (a^2+b^2)x^2+2(ac+bd)x+(c^2+d^2)=0 has no real roots then

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  19. The roots of the equation ax^2+bx+c=0will be reciprocal of each other ...

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  20. The roots of the equation ax^2+bx+c=0 will be equal in magnitute but o...

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