Question

Find all values of j for which the quadratic equation has one real solution.2x^2-7x+j=0Write your answer as an equality or inequality in terms of j.

Answer 1

The discriminant of a quadratic equation determines the number of real solutions for the quadratic equation.

if the discriminant is equal to 0, then it has only one real solution

$b^2-4ac=0$

a is equal to 2, b is equal to -7 and c is equal to j

$(-7)^2-4\cdot(2)\cdot j=0$

solve the equation for j

$\begin{gathered} 49-8j=0 \\ -8j=-49 \\ j=\frac{49}{8} \end{gathered}$