SOLUTION: Use the value of discriminant to determine the number and type of roots for the equation 2x^2-7x+9=0. Thank you

Question 41895: Use the value of discriminant to determine the number and type of roots for the equation 2x^2-7x+9=0.
Thank you
Answer by psbhowmick(878) (Show Source): You can put this solution on YOUR website!
Comparing the given equation with the standard quadratic equation we find a = 2, b = -7, c = 9.

The discriminant is .
Then if the coefficients i.e. a, b, c are real:
1) If D > 0, the roots are real but unequal.
2) If D = 0, the roots are real and equal.
3) If D < 0, the roots are imaginery and conjugate.

Special case:
If D > 0, D is a perfect square and the coefficients are also rational then the roots are also rational.

Here, = 49 - 72 = -23.
Hence, D < 0, also the coefficients are real and so the roots are imaginery and conjugate.
For a brief discussion on rational numbers you may see my lesson at
http://www.algebra.com/tutors/INTRODUCTION_TO_RATIONAL_AND_IRRATIONAL_NUMBERS.lesson?content_action=show_dev
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