Question
For each of the following quadratic equations, identify the values of \( a, b \), and \( c \). Use a positive value for a. \( \begin{array}{ll}\text { (a) } 2 x^{2}+3 x-10=0 & \text { (b) } 7 x^{2}=6 x-1\end{array} \)
Ask by Garrett Hardy. in the United States
Mar 01,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
For (a), a = 2, b = 3, c = –10.
For (b), a = 7, b = –6, c = 1.
Solution
For (a) the equation is already in the form ax² + bx + c = 0:
a = 2, b = 3, c = –10.
For (b) the given equation is 7x² = 6x – 1. To put it into the standard quadratic form, subtract 6x and add 1 to both sides:
7x² – 6x + 1 = 0.
Thus, in this equation:
a = 7, b = –6, c = 1.
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Simplify this solution Bonus Knowledge
For the equation \( 2x^{2}+3x-10=0 \), the values are \( a = 2 \), \( b = 3 \), and \( c = -10 \). For the equation \( 7x^{2}=6x-1 \), you can rewrite it in standard form as \( 7x^{2}-6x+1=0 \), giving you \( a = 7 \), \( b = -6 \), and \( c = 1 \).
