Question

Найти значения а, при которых уравнение ax^2-3x+2=0 не имеет корней

Answer 1

$a x^{2} -3x+2=0$

Дискриминант находится по формуле 
$D=b ^{2} -4ac$
Уравнение не имеет корней, если дискриминант меньше 0 
$D=(-3) ^{2}-4*2*a =9-8a\\\\9-8a\ \textless \ 0\\-8a\ \textless \ -9/*(-1)\\\\8a\ \textgreater \ 9\\ a\ \textgreater \ \frac{9}{8} \\ a\ \textgreater \ 1 \frac{1}{8}$

x ∈  $(1 \frac{1}{8} ; \infty )$

Answer 2

Ax²-3x+2=0
D=9-8a<0
8a>9
a>9/8
a∈(9/8;∞)

Answer 3

Finding the Values of 'a' for which the Equation ax^2 - 3x + 2 = 0 Has No Roots

To find the values of 'a' for which the equation ax^2 - 3x + 2 = 0 has no roots, we can use the discriminant (D) of the quadratic equation. The discriminant is given by the formula D = b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation.

- When D < 0, the quadratic equation has no real roots. - When D = 0, the quadratic equation has exactly one real root. - When D > 0, the quadratic equation has two distinct real roots.

Using the discriminant, we can determine the values of 'a' for which the given quadratic equation has no roots.

The discriminant (D) of a quadratic equation ax^2 + bx + c = 0 is given by the formula D = b^2 - 4ac.

From the provided search results, we can see that the discriminant (D) is used to determine the nature of the roots of a quadratic equation. When D < 0, the quadratic equation has no real roots. Therefore, to find the values of 'a' for which the equation ax^2 - 3x + 2 = 0 has no roots, we need to consider the discriminant D.

Using the Discriminant to Find the Values of 'a'

The discriminant (D) for the given quadratic equation ax^2 - 3x + 2 = 0 is calculated as D = (-3)^2 - 4*a*2.

To find the values of 'a' for which the equation has no roots, we need to solve the inequality D < 0.

The discriminant (D) is used to determine the nature of the roots of a quadratic equation. When D < 0, the quadratic equation has no real roots.

By solving the inequality D < 0, we can find the range of values for 'a' that will result in the given quadratic equation having no real roots.

Conclusion

In conclusion, to find the values of 'a' for which the equation ax^2 - 3x + 2 = 0 has no roots, we need to solve the inequality D < 0, where D is the discriminant of the quadratic equation. This will give us the range of values for 'a' that satisfy the condition of the equation having no real roots.