Question
\(4x^2-5x-12=0\)
Solution
Quadratic Formula Method
1
\( \text{Compare } 4 x^{2} - 5 x - 12 = 0 \text{ with the standard quadratic equation } ax^2 +bx+c = 0 \text{ and find the values of a, b, and c } \)
\( a = 4 \text{ , } b = -5 \text{ , } c = -12 \)
2
Calculate the value of the discriminant (D)
\( D = 217 \)
3
Determine the nature of the roots
The roots are real and distinct
4
\( \text{ Apply the quadratic formula } \)
\(x = \frac{5 \pm \sqrt{217}}{8}\)
5
\( \text{Find the roots of given quadratic equation } 4 x^{2} - 5 x - 12 = 0 \)
\( \text{The roots are } \frac{5 + \sqrt{217}}{8} \text{ and } \frac{5 - \sqrt{217}}{8} \)
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