Assignment for what value of \( R \) does the quadratic equation \( 3 x^{2}- \) \( 7 x+R \) has equal rooss.

For a quadratic equation in the form \( ax^2 + bx + c = 0 \) to have equal roots, the discriminant must be zero. The discriminant \( D \) is given by \( D = b^2 - 4ac \). In your equation \( 3x^2 - 7x + R = 0 \), we have \( a = 3 \), \( b = -7 \), and \( c = R \). Setting the discriminant to zero gives us: \[ D = (-7)^2 - 4(3)(R) = 49 - 12R = 0 \] Now, solve for \( R \): \[ 49 = 12R \implies R = \frac{49}{12} \] Thus, the value of \( R \) for which the quadratic equation has equal roots is \( \frac{49}{12} \).