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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 ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. a,b,c are positive real numbers forming a G.P. ILf ax^2+2bx+c=0...

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

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

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

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

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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^2+c^(prime))=0 and x is a r...

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

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