Math

QuestionFind the discriminant and number of real solutions for the equation 3x2+6x1=0-3 x^{2}+6 x-1=0.

Studdy Solution

STEP 1

Assumptions1. The quadratic equation is in the form ax+bx+c=0ax^{} + bx + c =0 . The coefficients of the quadratic equation are a=3a = -3, b=6b =6, and c=1c = -1
3. The discriminant of a quadratic equation is given by =b4ac = b^{} -4ac
4. If >0 >0, the equation has two distinct real solutions5. If =0 =0, the equation has one real solution6. If <0 <0, the equation has no real solutions

STEP 2

First, we need to compute the discriminant of the quadratic equation. We can do this by substituting the coefficients into the formula for the discriminant.
=b24ac = b^{2} -4ac

STEP 3

Now, plug in the given values for the coefficients aa, bb, and cc to calculate the discriminant.
=(6)2(3)(1) = (6)^{2} -(-3)(-1)

STEP 4

Calculate the discriminant.
=3612=24 =36 -12 =24

STEP 5

Since the discriminant is greater than zero, we can conclude that the quadratic equation has two distinct real solutions.
Discriminant24Number of real solutions2

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