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Let a,b,c be real. If ax^2+bx+c=0 has tw...

Let a,b,c be real. If `ax^2+bx+c=0` has two real roots `alpha,beta` where `alphalt-1` and `betagt 1`,then show that `1+c/a+abs(b/a)lt0`.

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Let `f(x)= x^(2)+ (b)/(a) x + (c)/(a)`.
According to the questions, we have the following graph.

From the graph
`" "f(-1) lt 0 and f(1) lt 0`
`rArr" "1 + (c)/(a)- (b)/(a)lt 0 and 1+ (c)/(a)+ (b)/(a) lt 0`
`rArr" "1+ (c)/(a)+ |(b)/(a)| lt 0`
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CENGAGE PUBLICATION-GRAPHS OF ELEMENTARY FUNCTIONS -EXERCISES
  1. Let a,b,c be real. If ax^2+bx+c=0 has two real roots alpha,beta where ...

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  2. Draw the graph of y= (1)/((1//x)).

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  3. (a) Draw the graph of f(x) = ={{:(1",",, |x| ge 1), ((1)/(n^(2)) ",",,...

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  4. Sketch the regions which points satisfy |x+y| ge 2.

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  5. Sketch the region satisfying |x| lt |y|.

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  6. For a point P in the plane, let d1(P)a n dd2(P) be the distances of th...

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  7. Draw the graph of y= (x-1)/(x-2).

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  8. The following figure shows the graph of f(x) =ax^(2)+bx +c, then find ...

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  9. The entire graphs of the equation y=x^2+kx-x+9 is strictly above the x...

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  10. If x^2+2a x+a<0AAx in [1,2], the find the values of adot

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  11. Draw the graph of f(x) = x|x|.

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  12. Draw the graph of the function: Solve |(x^2)/(x-1)|lt=1 using the grap...

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  13. Draw the graph of y = |x^(2) - 2x|-x.

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  14. Draw the graph of y = {{:(2^(x)",",, x^(2)-2x le 0 ),( 1+3.5 x- x^(2),...

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  15. Draw the graph of f(x)= |2x-1|+ |2x-3|. Find the range of the function...

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  16. Draw the graph of f(x) =y= |x-1|+3|x-2|-5|x-4| and find the values of ...

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  17. Find the set of real value(s) of a for which the equation |2x+3|+2x-3|...

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  18. Draw the graph of y= 2^(((|x|+x))/(x)).

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  19. Draw the graph of y= x ^((1)/(log(e)x)).

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  20. Find the number of solutions to the equation x+log(e)x=0.

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  21. draw the graph of f(x)=x+[x], [.] denotes greatest integer function.

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