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If x^2+p x+q=0a n dx^2+q x+p=0,(p!=q) h...

If `x^2+p x+q=0a n dx^2+q x+p=0,(p!=q)` have a common roots, show that `1+p+q=0` . Also, show that their other roots are the roots of the equation `x^2+x+p q=0.`

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CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
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  2. If a ,b ,p ,q are non zero real numbers, then how many comman roots wo...

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  3. If x^2+p x+q=0a n dx^2+q x+p=0,(p!=q) have a common roots, show that ...

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  4. a,b,c are positive real numbers forming a G.P. ILf ax^2+2bx+c=0...

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  5. If equations x^2+a x+12=0. x^2+b x+15=0a n dx^2+(a+b)x+36=0, have a co...

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  6. If x is real and the roots of the equation a x^2+b x+c=0 are imaginary...

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  7. Solve (x^2+2)^2+8x^2=6x(x^2+2)

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  8. Find the value of 2+1/(2+1/(2+1/(2+oo)))

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  9. If both the roots of a x^2+a x+1=0 are less than 1, then find the exha...

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  10. If both the roots of x^2+a x+2=0 lies in the interval (0, 3), then fin...

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  11. Solve (x^2+3x+2)/(x^2-6x-7)=0.

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  12. Solve sqrt(x-2)+sqrt(4-x)=2.

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  13. Solve sqrt(x-2)(x^2-4x-5)=0.

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  14. Solve the equation x(x+2)(x^2-1)=-1.

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  15. The number of distinct real roots of x^4 - 4 x^3 + 12 x^2 + x - 1 = 0...

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  16. Prove that graphs of y=x^2+2a n dy=3x-4 never intersect.

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  17. In how many points the line y+14=0 cuts the curve whose equation is x(...

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  18. Consider the graph of y = f(x) as shown in the following figure. ...

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  19. If x^2+p x-444p=0 has integral roots where p is prime number, then fin...

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  20. The equation a x^2+b x+c=0 has real and positive roots. Prove that th...

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