Answer:
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Class 10
>>Maths
>>Quadratic Equations
>>Solutions of Quadratic Equations
>>Find the roots of each of the following
Question
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Find the roots of each of the following equation, if they exist, by applying the quadratic formula:
16x
2
−24x−1=0
Medium
Solution
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16x
2
−24x−1=0
Compare given equation with the general form of quadratic equation, which is ax
2
+bx+c=0
a=16,b=−24,c=−1
Finding discriminant:
D=b
2
−4ac
=(−24)
2
−4(16)(−1)
=576+64
=640>0
Roots of equation are real:
x=
2a
−b±
D
x=
2⋅16
−(−24)±
64⋅10
=
2⋅16
−(−24)±8
10
=
4
3±
10
(Taking 8 common)
Roots are:
x=
4
3+
10
or x=
4
3−
10
Step-by-step explanation:
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