4x^2 - 6x + 2 = 0
a. find the value of the discriminate
b. find the exact solutions by using the quadratic formula.
show steps.

a. Discriminant = 4

b. x = 1 and

Step-by-step explanation:

The Sridhar Acharya Formula gives if ax² + bx + c = 0, the then the roots of the equation is given by

and

In this solution the term is called the discriminant of the original quadratic equation.

Now, in our case the equation is 4x² - 6x + 2 = 0

a. Therefore, the discriminant of this equation is = (-6)² - 4 × 4 × 2 = 4

b. The solutions of the equation are

and (Answer)

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°