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Find the discriminant. $\newline$ $5p^2 + 3p + 6 = 0$

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Using the discriminant

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Q. Find the discriminant.

\newline

5p^2 + 3p + 6 = 0

Identify values: Identify the values of $a$ , $b$ , and $c$ from the quadratic equation in the form $ax^2 + bx + c = 0$ . For the equation $5p^2 + 3p + 6 = 0$ , we have: $\newline$ $a = 5$ $\newline$ $b = 3$ $\newline$ $c = 6$
Recall formula: Recall the formula for the discriminant of a quadratic equation, which is $D = b^2 - 4ac$ . We will substitute the identified values of $a$ , $b$ , and $c$ into this formula to find the discriminant.
Substitute values: Substitute $5$ for $a$ , $3$ for $b$ , and $6$ for $c$ in the discriminant formula $D = b^2 - 4ac$ . This gives us: $\newline$ $D = (3)^2 - 4 \times 5 \times 6$
Calculate discriminant: Calculate the discriminant using the substituted values: $\newline$ $D = 9 - 4 \times 5 \times 6$ $\newline$ $D = 9 - 20 \times 6$ $\newline$ $D = 9 - 120$
Simplify expression: Simplify the expression to find the value of the discriminant: $D = 9 - 120$ $D = -111$

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