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If x is real and the roots of the equati...

If `x` is real and the roots of the equation `a x^2+b x+c=0` are imaginary, then prove tat `a^2x^2+a b x+a c` is always positive.

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CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
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  3. If x is real and the roots of the equation a x^2+b x+c=0 are imaginary...

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

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

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

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

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

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

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

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

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

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

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

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  18. If the roots of the equation x^2-ax+b=0y are real and differ b a quan...

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  19. If (a x^2+b x+c)y+(a^(prime)x^2+b^(prime)x+c^(prime))=0 and x is a rat...

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  20. Prove that the minimum value of ((a+x)(b+x))/((c+x))a ,b > c ,x > -c ...

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