Answer :
To find the value of [tex]q[/tex] such that the roots of the quadratic equation [tex]3x^2 - 5x + q = 0[/tex] are equal, we apply the condition for equal roots in a quadratic equation.
For a quadratic equation [tex]ax^2 + bx + c = 0[/tex], the roots are equal if the discriminant is zero. The discriminant [tex]\Delta[/tex] is given by:
[tex]\Delta = b^2 - 4ac[/tex]
In the equation [tex]3x^2 - 5x + q = 0[/tex], we have:
- [tex]a = 3[/tex]
- [tex]b = -5[/tex]
- [tex]c = q[/tex]
The condition for equal roots is:
[tex](-5)^2 - 4 \cdot 3 \cdot q = 0[/tex]
[tex]25 - 12q = 0[/tex]
Solving for [tex]q[/tex], we rearrange the equation:
[tex]25 = 12q[/tex]
[tex]q = \frac{25}{12}[/tex]
Therefore, the value of [tex]q[/tex] that makes the roots of the equation equal is [tex]\frac{25}{12}[/tex].
The chosen multiple choice option is (4) [tex]\frac{25}{12}[/tex].