Comparing the given equation 2x² - 4x + 3 = 0 with the standard form ax² + bx + c = 0, we find the coefficients a = 2, b = -4, and c = 3.

We evaluate the discriminant using D = b² - 4ac. Squaring -4 gives 16, and subtracting 4 × 2 × 3 = 24 yields D = -8.

What is the nature of the roots of the quadratic equation $2x^2 - 4x + 3 = 0$ ?

Answer: No real roots (or two distinct complex/imaginary roots)

Step-by-step solution

Step 1: Identify coefficients

Comparing the given equation $2x^2 - 4x + 3 = 0$ with the standard form $ax^2 + bx + c = 0$ , we find the coefficients $a = 2$ , $b = -4$ , and $c = 3$ .

Step 2: Calculate the discriminant

We evaluate the discriminant using $D = b^2 - 4ac$ . Squaring $-4$ gives $16$ , and subtracting $4 \times 2 \times 3 = 24$ yields $D = -8$ .

Step 3: Determine the nature of roots

Since the discriminant is strictly negative ( $D < 0$ ), the quadratic equation has no real roots (the roots are distinct complex or imaginary roots).

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What is the nature of the roots of the quadratic equation 2x2−4x+3=02x^2 - 4x + 3 = 02x2−4x+3=0?

Step-by-step solution

Step 1: Identify coefficients

Step 2: Calculate the discriminant

Step 3: Determine the nature of roots

What is the nature of the roots of the quadratic equation $2x^2 - 4x + 3 = 0$ ?