Sign of discriminant decides the property of solutions of a quadratic equation. A quadratic equation having 30 as its discriminant will have: Option C: Two solutions.
How to use discriminant to find the property of solutions of given quadratic equation?
Let the quadratic equation given be of the form ax^2 + bx + c = 0, then
The quantity [tex]b^2 - 4ac[/tex] is called its discriminant.
The solution contains the term [tex]\sqrt{b^2 - 4ac}[/tex] which will be:
- Real and distinct if the discriminant is positive
- Real and equal if the discriminant is negative
- Non-real and distinct roots
There are two roots of a quadratic equations always(assuming existence of complex numbers). We say that the considered quadratic equation has 2 solution if roots are distinct, and have 1 solutions when both roots are same.
For the given case, it is specified that the discriminant is 30 > 0, thus, its roots are real and distinct.
Thus, two solutions exist for such quadratic equations. (option C)
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