Question

The equation \( 3x^2 - 5x + 2 = 0 \) has

• A. two real and unequal roots
• B. two real and equal roots
• C. no real roots
• D. None of these

Hint:

The nature of the roots of a quadratic equation \( ax^2 + bx + c = 0 \) is determined by the discriminant \( \Delta = b^2 - 4ac \): - If \( \Delta > \), two distinct real roots. - If \( \Delta = 0 \), two real and equal roots. - If \( \Delta <\), no real roots (two complex conjugate roots).

Answer 1

The Correct Option is A

Step 1: Identify the coefficients.
The given quadratic equation is \( 3x^2 - 5x + 2 = 0 \), where \( a = 3 \), \( b = -5 \), and \( c = 2 \). Step 2: Calculate the discriminant.
The discriminant is \( \Delta = b^2 - 4ac \). \[ \Delta = (-5)^2 - 4(3)(2) \] \[ \Delta = 25 - 24 \] \[ \Delta = 1 \] Step 3: Interpret the discriminant.
Since \( \Delta > \), the quadratic equation has two distinct real roots, which means two real and unequal roots.