Question

18. Find the values of K for which the quadratic equation 2x+3x+K = 0 has real roots.​

Answer 1

       $\underline{\bold{Given-Equation:}}$

       $2x^{2} + 3x + K = 0$

       $\underline{\bold{To-Find:}}$

       $\text{The value of }K \text{ for which the given equation has real roots}$

       $\underline{\bold{Previous-Knowledge:}}$

       $\text{For a quadratic equation, of the form }ax^{2} + bx + c = 0, \text{ to have}\\\text{real roots, the value of } b^{2} - 4ac \geq 0$

       $\underline{\bold{Solution:}}$

       $b^{2} - 4ac \geq 0$

       $\text{Substituting the values from the equation}$

$\implies (3)^{2} - 4(2)(K) \geq 0$

$\implies 9 - 8K \geq 0$

       $\text{Adding } 8K \text{ to both sides}$

$\implies 9 \geq 8K$

       $\text{Dividing by 8 on both sides}$

$\implies \boxed{\frac{9}{8} \geq K}$