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Here we have to find the sum and product of the roots of the equation 2x^2+5x+9=0. Instead of first calculating the roots and then adding and multiplying them, let us use Viete's relation:
We have the sum of the roots as -b/a and the product of the roots as c/a
Here a = 2, b= 5 and c= 9
Therefore the sum of the roots is -b/a = - 5/2 and the product of the roots is c/a = 9/2.
The required sum and product of the roots are - 5/2 and 9/2 resp.
2x^2+5x+9 = 0
To find the product of roots:
If x1 and and x2 are the roots of the equation , then by the relation between the roots and and the coefficients of the equation, we get:
x1+x2 = -5/2
x1*x2 = -9/2= -4.5.
Therefore the product of roots = -4.5.
We have2(x+5/4)^2>=0 when x=-5/4
the minimum is 47/8 when x=5/4
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