Question

При каких значениях p уравнение имеет один корень ,два корня;не имеет корней : х^2-8х+3+р=0

Answer 1

Уравнение ax²+bx+c=0
имеет
1) 1 корень, когда дискриминант (D) = 0.
2) 2 различных корня, когда D>0,
3) не имеет корней при D<0
D=b²-4ac
D=(-8)²-4*1*(3+p)=64-12-4p=52-4p
1) 52-4p=0
4p=52
p=52:4
p=13
2) 52-4p>0
-4p>-52 |:(-4)
p<13
3) 52-4p<0
p>13

Answer 2

Equation Analysis for x^2-8x+3=0

To determine the number of roots the equation x^2-8x+3=0 has, we can analyze the discriminant (D) of the quadratic equation ax^2 + bx + c = 0, where a, b, and c are constants.

Discriminant (D) Analysis: - The discriminant (D) is given by the formula D = b^2 - 4ac. - If D > 0, the equation has two distinct real roots. - If D = 0, the equation has exactly one real root. - If D < 0, the equation has no real roots.

Applying the Discriminant Analysis to the Given Equation

For the equation x^2-8x+3=0: - a = 1, b = -8, and c = 3.

Calculating the Discriminant (D): D = (-8)^2 - 4*1*3 D = 64 - 12 D = 52

Conclusion: The discriminant (D) for the given equation is D = 52, which is greater than 0. Therefore, the equation x^2-8x+3=0 has two distinct real roots.

This analysis indicates that the given equation has two real solutions.